こんにちは

俺はアメリカ人と日本語は吸う。
My Japanese sucks and I'm American. Please tell me if I just accidentally said Japanese sucks...

I do not really grasp what you are trying to say.
The expression "sucks" as in, "you are bad at something" do not exsist in Japanese, but nice try though :D

If you want to say that your Japanese is bad, you say 日本語がへた

So

こんにちは
俺はアメリカ人で、日本語がへた（and usually, you write へた in kanji, so you write 下手）。 

Hello! I am American and my Japanese sucks.
You do not use "と" as "and" in this context, but "で" which is a way to continue a sentence after a noun.

And I would recommend you to use politer Japanese, even if the sentence above is grammatically correct.