Hello, you could use both "tan" and "get tanned" in this way:
1. "tan" as a noun, is a "thing", for example "I'd like to get a tan when I go to the beach next weekend."
You would say "a tan" because it is a noun, a thing.
2. "to tan" as an action or verb: " I want to get tanned this weekend, I have been indoors too long!" or "With this lotion I think I can get tanned easily."