If any of your interests are something people typically get social about (anime, gaming, chess, dining, pets) there's probably groups in your area. For people who have trouble starting conversations, these can be very helpful as you'll be meeting regularly over a common ground. I think if you have to sit down on opposite ends of a chess board, you'll have to talk about something a little more interesting than bad pick up lines or the weather eventually. People who want someone to meet them at the dog park and keep them company while their pets have a play date could easily turn out the same way.
Definitely check meetup.com.
For anyone reading who has problems with anxiety, there might even be support groups locally.