It depends on your goal, so your question might be too broad.
If you want to show your real face, but at the same time don't want your face to be analyzed by any AIs, then it's impossible, because your face will be processed by some AI sooner or later. Even if a particular social media site didn't use AI at the moment, it might start doing so in the future.
If you want to look like a typical social media user, but at the same time you don't want to show your face, you could take pictures of you from a distance or from behind. Only some features should be visible (your hair, your ears, etc.), maybe too small and in low resolution, maybe even a bit distorted / noisy / pixelated because of darkness or some filter. For example, a picture like this looks very cool, yet the woman can't be easily recognized.
If you want to use somebody else's face, you could use AI-generated faces like those at thispersondoesnotexist.com or on this other webiste. Depending on your needs, you could use such pictures in their original form, or you could edit them to create an artistic avatar (using filters, colors, etc.), or you could even try to find an AI-generated face that looks a bit like yours, edit your pictures to replace your face with the AI-generated one, etc. Note that not some social media platforms might be able to spot these tricks, or might be able to detect them in the future anyway. See this article about Facebook removing fake accounts for example, and this other one about Facebook interested in deepfake detection.
A final warning about anonymity and privacy on social media: note that if, for example, you sign up on Facebook and don't ever upload a picture of yours, Facebook might still be able to know who you are exactly. How? Well, if when you signed up you provided your phone number, and you also use that phone number for WhatsApp (owned by Facebook), Facebook could put all that information together and know who your friends are, who are the ones you message the most, collect all their profile pictures (including yours on WhatsApp, etc.). So the bottom line is that some social media platforms are not privacy friendly at all and should not be used if you are really concerned about your privacy. Some social media are not meant to be used by privacy aware people.