I just put a new alternator on my car I didn't notice a ground cable. There is the green plug going into it and the wire for the battery but that's it is the bracket grounding it or the green plug have a ground in it? the engine is a 97 integra ls.

 

It will be grounded being bolted into the motor. The plug may or may not have a ground wire in it. Either way, it will be grounded