It would be a good idea to bring a gift with you to an engagement party. Most people find it courteous to do this. Look for something that the couple will definitely love as it would remind them of that day. However, it is not mandatory to bring a gift.
Just because you are invited to a function, doesn't obligate you to bring a gift....however, it is considered standard courtesy if attending said event to show your thanks by bringing something for the host or hostess, or guest of honor in this case. For engagement, probably something small...no need to go super lavish just yet. Not a shower type gift unless you won't be attending any...remember they supposedly haven't started their lives together yet! If the party has a theme...get something that goes with the theme...My engagement party was "HOT Things" themed (sister and parents decorated with peppers, and served fajitas!)....favorite gifts were chili pepper patio lights, and a grilling apron with "Hot Stuff" on it! We also got bottles of hot sauce, pot holders, etc.