Can I do a portrait photography career with an iPhone?

I can do it with an iPhone that looks rather professional, imo. I've practiced on a few of my family. Sure, there can be more improvement which requires practice.

No. Just compare the image size. On my phone, images are usually about 1.3 MB. But on my real camera, they're closer to 7 MB. The extra size means more quality.

Career? As in a lifelong stream of flowing income? Using nothing but an iphone? Dream on.

"IMO"?

No, you need a better camera to be a professional.

The very fact that you need to ask that question must surely suggest to you the most likely answer!

Has anyone asked to purchase one of your photographs from your iPhone? No? Well, there's your answer!

Yes, if your specialization is portraits for social media. Camera phones have improved greatly. However, they are still limited by the physics of small optics and sensor. You will get better quality photos that are suitable for large prints from a camera with a larger lens and sensor.

The other aspect is the client's expectations. It is true that a skilled photographer can get good photos from a cell phone and an unskilled photographer will get poor images from a Hasselblad. However, the consumer will perceive the larger camera as more "professional".

No. Simply because the lens in a smartphone is wide angle. Wide-angle lenses should never be used for portraiture because they distort the facial features making people look ugly. You must use an interchangeable lens camera such as a DSLR or a mirrorless, but never a smartphone.

The new iPhone 11 has a 52mm (35mm equivalent) lens, but that's is still too short. You need to be using a focal length somewhere between 85mm~200mm for portraits in order to flatten the perspective which makes people look more attractive than they do in real life. The lens in smartphones has way too much distortion making it the worst possible camera for portraiture.