Best thing to do is look around at the programs you currently belong to and see if Avis is a partner. For me, I signed up via British Airways Executive Club and got some bonus miles for joining, plus an Avis upgrade voucher to use on my first booking. You can get that at AvisBA.com.
Generally you don't get much just for joining though, but you'll get rewarded the more you use them. I frequently get offers directly from Avis as well as BA & Amex for Avis rentals.