Though cat pictures are less prevalent, it's not rare for applicants put a small headshot in the corner of their resumes. Unless you’re an actor, pictures do NOT belong in a job application. First of all, the hiring manager is going to look you up on social media anyway, so if you really want him to see what you look like, rest assured, he will. But more to the point, adding a photo to your resume is unprofessional. It suggests that you are expecting to be hired based on your looks instead of your skills, and this can definitely backfire.
Don’t let a picture distract from all the awesome qualities you’ve listed on your resume. But DO put a picture on your LinkedIn profile. It adds credibility and will earn you more profile views.