Of course you can take your headshot with your cell phone.Trust me on this, you won't look your best if you do. Your cell phone is configured to grab as much of a scene as possible.
It's set to take wide angle photos. Wide angle lenses tend to exaggerate facial features. That's why your nose always look super wide in selfies. Do yourself a favor and hire a professional. If you are job hunting or selling something the small investment is a great photo is worth it.
I always use external lighting when making a headshot. Before I deliver the photos to my client I'll color correct and remove any obvious flaws in the skin.
Do you include your head shot photo on your resume?