Can I activate the tap ability of a creature summoned last turn before I have to remove it to my hand?
Yes, he can do this. The rule for summoning sickness is as follows:


  302.6  A creature’s activated ability with the tap symbol or the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since his or her most recent turn began. A creature can’t attack unless it has been under its controller’s control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.


Emphasis mine. In this case, the creature was under his control continuously since his most recent turn (which is the current turn) began.