Using Titanium as antenna in implantable tracking system
The wire should be insulated, and the insulation needs to be biocompatible.  The conductor need not be biocompatible.  

Frankly, the environmental demands on such systems can be impressive and surprising to someone that hasn't used them. Keeping in mind that device failure would mean unnecessarily inconveniencing an animal, I'd recommend going to the pros, like http://www.telonics.com/wildlife.php  or http://www.blueskytelemetry.co.uk/wildlife_tracking.asp

Whoever is running the investigation will have an easier time getting the study through a review committee if you take that approach.