The answer for anyone applying inside the United States is no, and it has almost nothing to do with how you look. It is about how resumes get handled, first by software that reads them as text and then by people who have been asked not to look at your face. Here is the whole picture, including where the photograph does belong.

If you are applying for a job in the United States, leave the photograph off the resume. There are two separate reasons and neither one is about vanity. Employers here commonly ask the people who screen applications not to weigh appearance, and some remove images from a file before it circulates internally, so at best the picture is ignored and at worst it makes your application awkward to pass along.
The second reason is mechanical. A resume is a text document that gets read as text, and an image is not text. It adds weight, it survives the trip badly, and it usually arrives inside the kind of decorative layout that causes the rest of your file to be misread. Put the photograph on your profile, your own site, your signature and your bio instead, where it is expected and where it actually works.
I am a photographer, not an employment adviser, so take this as an account of the convention rather than counsel about your particular situation. The convention is clear enough. In the United States, the resume is treated as a record of what you have done, and appearance is deliberately kept out of that record.
The reasoning is about risk and fairness rather than taste. An organization that wants its hiring decisions to rest on evidence will often instruct the people doing first-pass screening to disregard anything about how a candidate looks. Some go further and prefer that files circulate without photographs at all, so that nobody downstream can be accused of having weighed the wrong thing. None of that is a rule aimed at you. It simply means your photograph, arriving uninvited, creates a small handling problem for the person who receives it.
There is a softer version of the same point. A photograph on an American resume signals unfamiliarity with the local convention. That is a fair thing to be, especially if you trained somewhere the convention runs the other way, but it is a signal you did not intend to send and it is entirely avoidable.
Before a person sees your file, something usually extracts the text from it and drops that text into fields: name, employers, dates, titles, skills. That extraction is the part everybody forgets, and a photograph interacts with it badly in ways that have nothing to do with the picture itself.
The honest summary is that the picture is not usually rejected. It is simply dropped somewhere between your desktop and the reader, while the design decisions made to accommodate it stay behind and cause damage. That is a poor trade for something you did not need on the page.
A resume is usually one page, occasionally two, and the top few inches are the part that reliably gets read. A photograph sits in exactly that region.
Work out what it is displacing. In that same block you could carry a real title line, a two-line summary of what you do and for whom, or the single strongest result you have ever produced. Any of those does more for you than a picture that the reader has been asked to disregard.
This is the argument I find most persuasive, because it does not depend on any employer's policy. Even in a world where photographs on resumes were entirely normal, the photograph would still be the least informative thing you could put in the most valuable space on the page.
There are real cases where a photograph belongs with the document, and pretending otherwise would be as unhelpful as the blanket advice it replaces.
Here the picture is the document. The convention is a printed portrait with the resume attached to the back, trimmed to match, and the photograph is the credential being submitted. Nobody in that field considers it a resume photo in the sense this page is about.
Plenty of countries expect a portrait on a CV, and in some of them leaving it off looks careless. The test is not your nationality, it is where the job sits and who is hiring for it. A role based abroad, hired by a team abroad, follows the convention there. A US-based company hiring for a US-based role follows US practice even if the parent organization is somewhere else. When you genuinely cannot tell, leave it off and put it on your profile, which is visible to everyone either way.
Generally no photograph on the CV itself. The portrait belongs on the department page, the faculty directory and the profile that a search committee will look at anyway.
A one-page bio for a speaking submission, a board packet, a capability sheet, an agent's personal marketing page: these are marketing documents and they take a portrait, because the whole point of them is that a person is the offering. If you are assembling one of those, the relevant question is not whether a photograph belongs but which one, and that is answered by the same thinking as professional headshots generally.
If a recruiter or an employer requests a photograph, send one. Someone asking has removed the awkwardness, and refusing on principle is a strange hill to choose.
Nothing here argues against having a good portrait. It argues about placement. During a job search the picture is doing more work than the resume ever could, just not on the same sheet of paper. I have written the search-specific version of this in headshots for job seekers.
The full inventory of places one sitting has to serve, and how to size and crop for each of them, is in how to use your headshots everywhere.
Send it as a separate file or a link, never embedded in the resume. That keeps the document clean and gives the person on the other end something they can actually use.
Send a current portrait on a plain background, cropped conventionally: head and shoulders, eyes in the upper third, no group crops and no vacation frames. The same description holds whether the request came from an employer abroad, a casting call or somebody assembling an internal introduction, because all three want to see the person rather than a scene.
If the request came with a purpose attached, a program page, a panel listing, an internal introduction, ask what shape they need. A vertical portrait and a horizontal version of the same look cover nearly everything that gets asked for in practice, which is one of the reasons a sitting is planned around more than a single frame.
There is a genuine instinct underneath the question. You want the person on the other end to remember you as a human being rather than a set of dates, and a face does that faster than any bullet you could write.
The instinct is correct. The placement is what fails. A photograph on the resume reaches the one reader who has been asked to ignore it, inside a document nobody keeps. The same face on your profile and in your signature reaches everyone who looks you up, and stays visible long after the file is closed.
So do the thing the impulse is pointing at, and do it where it counts. Get a portrait made that actually looks like you on a good day, put it on every surface that carries your name, and let the resume be one clean page of evidence. Making that portrait is what headshots are for. The resume simply stops being the place it lives.
The resume stays a page of evidence and the photograph goes everywhere else your name appears: profile, site, signature, bio. If you are in a search and that portrait is the piece you have been putting off, call me at (239) 319-6171 or send the form, and we will plan what the picture has to do before anyone points a camera at you.
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