Translation:I want to be a police officer.
Actually, the meaning would be different because 想 means both "want" and "think". 我想做一个警察 means “I WANT to be a police officer,” while 我想是一个警察 means "I THINK it's [or he's or she's] a police officer."
So you would infer an unstated "he/she" if 是 is used, but not if 做 is used? Is there any rule to know when to apply that kind of inference or is it just a result of practice?
Good question. 我是 means "I am," of course. 我做 means "I do" or "I make." However, starting a sentence with 做 can mean "being." Using any verb alone can answer a question in the affirmative ("Yes") if that is the verb in the question, but 是 alone is the generic word for "Yes." So 是 is a special verb, kind of like how "be" is unique in English.
I believe 我想当一个警察 is probably a better way to say this for those new to the language. The use of 当 which in this case means "to become" seems less confusing.
Lol, who else thought that maybe the speaker wants to do some police officer? Or at least make a new one :D