행복하자 correct?
Hello, I apologise if this is the wrong place to ask, but my korean notions are still very shallow and I don't know where else I can turn to. I am planning to get "행복하자" tattooed as a reminder to strive for happiness, to be open-minded about foreign cultures and that music can always be a safe place (it's a line from a song, yes). Is it grammatically correct? Does it sound awkward or is it okay?
This is very important to me, thank you very much for reading and perhaps answering. Again I am sorry if this is a bad place to ask. Have a nice day!
EDIT; thank you everyone for the answers!!

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its incorrect grammatically but its not so weired
there's a lot of song that title is '행복하자'

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How about using "행복하다" or "행복해요" instead of "행복하자"?
"행복하다" or "행복해요" means "(I am) happy (now)."  or "(We are) happy (now)."  It indicates the current state of happiness. 
Or you can use "행복해". 
"행복해" means the same thing as "행복해요" but it sounds like talking to yourself " I am happy or we are happy."  It also sounds like saying "Be happy" to your friends.

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You can also say 행복해지자. but I would probably do 행복하자 IF I ever only want to follow the trend and stuff.
:-) Hope you become happier everyday!

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행복하자 is grammatically incorrect.
행복하다 is an adjective.
An adjective cannot be used as imperative or  suggestive form.

Even if it is grammatically incorrect, some Korean people use that phrase.

cf.
행복하게 살자 or 행복하게 지내자 grammatically correct.