The literal translation would be something along the lines of "Ich möchte mich MIT DIR in Verbindung setzen", so the whole phrase would be:
"Ich möchte mich mit dir in Verbindung setzen, um dir alles Gute zum Geburtstag zu wünschen."
As you can see, I've changed the end of the sentence as well to get it closer to German standards, since nobody would wish a good/ happy birthday over here but rather "all the best".
Hope that clears things up! :)