Yes, you have several opportunities to cast spells and activate abilities during the combat phase.
The combat phase is divided into several steps:
506.1. The combat phase has five steps, which proceed in order: beginning of combat, declare attackers, declare blockers, combat damage, and end of combat. The declare blockers and combat damage steps are skipped if no creatures are declared as attackers or put onto the battlefield attacking (see rule 508.8). There are two combat damage steps if any attacking or blocking creature has first strike (see rule 702.7) or double strike (see rule 702.4).
At the start of each step (except end of combat), certain turn-based actions happen. At the end of each step, each player gets priority (the right to cast and activate abilities) in turn order before the game proceeds to the next step.
So as long as your vigilance attacker is on the battlefield, you can activate its ability. The Tap symbol in an ability's activation cost only means that the creature has to be untapped and without summoning sickness. It doesn't matter whether or not it's attacking.