Yes, you can paint an aluminum door. Although you can paint it with almost any paint, an exterior spray-paint leaves a nice smooth finish without any brushstrokes, and it dries fast and adheres better than latex. There are many color choices available at home improvement stores. Good luck!
You cannot use latex paint on aluminum. There's a chemical reaction between aluminum and latex that will cause it to bubble and peel in very short order.
I painted the exterior of an entire aluminum camper as follows:
1) sand off any peeling paint and white bloom.
2) wash with TSP, rinse, dry
3) treat any bare aluminum with ALUMINUM primer. This is different than typical metal primer and it will specify aluminum on the label
4) paint with a direct to metal paint. I used PPG full acrylic DTM paint.
This was painted over two years ago, has been exposed to the elements full time and was subjected to multiple hail storms. There aren't even any scratches or fading.
Great article. A common error even professionals make. Full acrylic paint is not latex. Full acrylic paint does not contain vinyl whereas acrylic latex has a combination of acrylic resins and vinyl. The key is ammonia content of the paint. Ammonia and aluminum are reactive. https://todayshomeowner.com/how-to-paint-aluminum-siding/