Can we invite our parents to an engagement party at a restaurant

If it's just you and your parents going out to dinner I wouldn't really consider that an engagement party, but it sounds like a nice idea! Typically an engagement party is hosted by someone else (often your parents), throwing one for yourself could be seen as gift-grabby. It's not necessary to have an engagement party, I didn't.

View Quoted Comment Thank you! I wasn't sure what all was needed and if that was even a thing. I just want everyone(meaning are parents) to meet eachother. It was something I thought would be nice. I'm just not sure what it is...

If I'm understanding you correctly, you would like to introduce all the parents to each other. At that time you would tell them you are engaged. Correct?

There's no reason to give such a meeting a name. Just say, "mom and dad, I'd like for you to meet fs's parents. Would Friday at X restaurant work for you?" I will say, as a mom, if you can't schedule something very soon, the next week and a half or so, I'd let all parents know of the engagement before hand. I'd still have the time to introduce them to each other.

This is definitely more like an engagement announcement than a formal engagement party! I see nothing wrong with the idea, it seems like a nice way to tell the people you are close with!

I don't know if I would tell them you are engaged like this. Parents have all sorts of emotions about engagements. Tell them separate then do dinner.

That's a great idea! I'd just plan a special dinner and invite them, I don't even know if I'd call it a party. My FMIL took us out after we got engaged with my fiance's side of the family and it was very nice.