Gideon avenger

[Jazzeligman]

Can I tap a creature with Gideon avenger on the opponent turn, and forcing him to not attack with that specific creature?

[BlackJester]

You can use {Gideon's Lawkeeper} to tap a creature your opponent controls, yes.  {Gideon's Avenger}, not so much.

You have the opportunity to use instants and activated abilities during the Beginning of Combat Step.  If they have already declared their attackers then it is too late.