Using Rengar Legend, if I play a unit and it is my only unit, can I give it to himself his +1?

Yes, you can give the +1 Might bonus to the unit you just played.

According to the rules for Rengar, Pridestalker (the Legend), its ability reads: "When you play a unit, give a unit +1 [S] this turn."

When you play a unit and it is the only unit you control, you are the one choosing the target for the ability. Since the ability says "give a unit," and does not specify "another unit," you are permitted to choose the unit you just played as the target for the +1 Might bonus.