Unfortunately at 16 I don't know that you can have a direct impact on this. No 16 year old is going to want to hang out with someone because their parents told them to or set it up.
I would suggest encouraging him to find people who share his interests. Comic book shops and table top gaming stores are a haven for teenage/young adult boys who are socially awkward. Many of them have gaming tournaments for card battle games, strategy games, roll playing games and some do video game tournaments too. If you have something like that in your area, maybe you could drop him off there for 30 minutes or so and just encourage him to look around and see if anything there interests him.
You might also check with his school to see if there are clubs he might be into. For example, our high school has a great robotics club.
It seems like if he could just find people who are interested in similar things, it would go a long way toward making him feel more comfortable.

My son is now 13. He has ASD at a moderate level but does display certain behaviors from time to time. He reads and write and is also in his middle school band for the 2nd year. I am so proud. He and my older son (16) are very, very close. I almost felt that my son depended on him a little too much in the earlier years. In the beginning, in his earlier years. He was not interested in making friends at all. He always felt that other kids were cruel and lacked respect for one another. So he would say "I don't want friends like that". Amazing to me, was for him to have been thinking this way at such a young age. However, last year I asked him if he made friends with anyone (as I would ask every school year) to my surprise he mentioned one boy from his class who helps/aids him during class time. He told me that he liked him and trust him. He also ask if the the young man could come and visit at the house. I was elated, you don't know how happy I was to hear my son wanting a friend. So I'm saying mother's don't give up. Your kids have a very special insight on life. Believe me, I've cried and have worried about what's to become of my son in his adult years. I know I'm not going to always be here to protect him and guide him as I do. But, I'm working hard to help him gain confidence in himself and understand that the world can sometimes be cruel but there is a place for him in it.

I'm a 48 year old autistic. Most of my friends when I was in school were from academic clubs. We're smart and being around people who respect intelligence really helps. I was in the chess club, the math club, science explorers and medical explorers.

For years, I had a lot of trouble understanding 'NT' people, then I discovered Dale Carnegie's "How to win friends and influence people." This book explained people and provided a 'System' of rules on how to successfully interact.

It helped me a lot.

HTH

Gene

I went through this with my son too (he is highly verbal and social). Ask yourself does your son WANT friends- my son had little to no interest until 4th or 5th grade. I would arrange play dates and he was rarely engaged with the "friend". It took four years of social skills groups and camps before he had the comfort level needed to interact with his peers.

During thise years I realized that what was causing me pain (on his behalf) he was oblivious to.

He is 12 now and has some friendships through school and extracurricular activities (he's in the school play and does a couple other after school clubs). The other thing I had to learn is that boy friendship is not the same as girl friendship- girls have bff's, boys have guys that razz them daily. Girls hang out and talk and talk and talk. Boys sit beside one another in front of a video game or comic book and occasional make a comment (often to get a reaction from one another).

As the others have said, your best bet is find groups that are centered around his interests. Meetup.com is a good place to start.