Would it be possible for someone to do diy acupuncture on your own face?

Trained: If you are adequately trained in the art/ practice of acupuncture - you can provide self treatment. I do. I wouldn't go around poking yourself in the face with needles if you don't know what you are doing.

Yes for therapy!: Not for cosmetics. Yes, in a few cases, where it's inconvenient for travel or work restrictions or the patient just can afford the cost, they need lots of dry needling to decrease trigger point density; they are comfortable with self needling and prove to me that they have steady hands and the involved area has no critical arteries, nerves or organs. I call this "needling", not acupuncture.

Possible yes: Advisable no. You "can" also do you own abscess drainage, skin suturing, and skin tag removal, but these are other instances that unless there isn't any other option available I would encourage you to seek out the expertise of a trained professional.