You aren't likely to find a regular daycare that allows a non-vaccinated child to attend. You may, however, find someone who runs a small in home day care that will allow it. Most bigger daycares are simply too fearful of liability problems to deal with non vaccinated children. (Funny since the other vaccinated children shouldn't be at anymore risk *IF* vaccines worked as advertised.)
Personally, since you've done such a great job keeping your child out of daycare thus far, I wouldn't use it just for socialization. How about, instead, finding a local playgroup or routinely going to a local park so you get to know the 'regulars'? I know meetup . com has all sorts of playgroups you can join. Perhaps your church does a mom's morning out you could participate in? Or you could form a co-op with a few friends where each of you watches the group of children one morning per week so the other moms have some time to run errands and the kids get to play together.
If the goal is just socialization, there are many options other than daycare. My 22 month old son has never been to daycare and won't be going to such a place fortunately. He does however get out and play with other kids about 3 times per week through various playdates with friends or going to local parks and splash pads. His social skills are great and he has lots of confidence when dealing with new kids. :)