A Part of ...

"I am a part of the team" implies that you are an individual composing a part of the whole, which also implies that the whole is a composite. "I am part of the team" implies that the team is an entity of its own, and you contribute to that whole.

Basically, the first is more focused on the "I" while the second is more focused on the "team." Both are correct.

I could not describe this reasoning more beautifully than the post above. But, take into consideration that many times in English, sentences are shortened to save time and space. Therefore sometimes small articles like "a" and "the" can be deleted with the same meaning being implied. I know, it's so confusing. But usually when kids learn English in schools, the teachers usually tell them to listen to other people having conversations, or when you read, read outloud. Soon you will have an "ear" for the English language. In a way, you will be able to tell what things "sound right" and what things "sound wrong."