You can pretend to be smart. Not to be social (well, kind of)
First, let me talk about a related issue. It is common for players and GM to have trouble accurately playing a character smarter than them. One reason for that is that unfortunately, becoming smarter is pretty difficult. Some would argue that if you aren't born smart, there isn't much you can do. Some would say that a good education could help, but otherwise, you screwed all the same. So you have to fake it.
Then what about social skills?
Bad news: unfortunately, there are less tricks to fake a social character. Fortunately, it is easier to learn.
Yes, YOU will have to become social. Like, really.
Yup, you will actually have to improve your own social skills. It will bring you a great return on investment, as you will learn how to play a character with good social skills, but also will be better at playing a total boor, since you will know exactly what NOT to do. It might also make your personal life better, which is quite nice.
Obviously, it is a long process, but at least it is possible, so here are some hints on what social people often tend to do. This doesn't mean that everyone doing those is the new MLK, but those are things that people deemed charismatic will often tend to do.
Again, a lot of people talk fast, in order to make sure people hear what they say. Unfortunately, it has the opposite effect, as by the time the audience register you started speaking, you are done already. Also, if you talk fast, you imply that what you are saying isn't worth the time.
Respect your words and what you are saying: talk slow. Make breaks in your sentences, and so on.
Politicians are really good at that. Observe them.
You believe strongly in anything you say, so say it with all the passion you have. Accentuate a lot. Don't go:
"I think we should make an alliance with the druids yeah."
"Me? Me, I see the children out there. The children. I see them fighting, fighting their friends, fighting their families, and for what?! (pause) For food?! (pause) And we all know that an alliance, a simple alliance with the druids would solve all of those issues, would bring food to the streets, would save this city's sons, and I think: why haven't we done it yet?"
Eye contact is really powerful, and the longer you can hold it the better. Practice as much as you can, until it becomes totally comfortable for you. You might end up staring for a while, so keep going until you can look straight into someone's eyes without looking creepy, or panicked, or whatever. You might also be surprised how other people have trouble with it.
Use your hands
When you speak, use your hands to accentuate what you say. If your hands are resting on the deck or in your pockets when you speak, you are doing something wrong.
Smile as much as you can, and get comfortable with it. Overall, the more facial expressions you can do, the better, but smiling is one of the best things, it makes everything you say more powerful.
Call People By Name.
Very powerful, makes everything you say immediately more important and personal. There is a world of difference between this:
How are you doing?
How are you doing, Samantha? (if your name is Samantha; else it's just awkward)
Other body language tips
Stand straight. Even if a character is slouching in a throne, keep your back straight and head high. Keep your arms/legs wide, to take space. If you want to have 'social advantage' over someone, avoid facing them, and instead keep a ~30 degrees angle with them. Oh, and stop fiddling with you rpen, or hair, or dice, or whatever.
As mentioned above, observe how actors and politicians speak. Start with Bill Clinton, who is often described one of the most charismatic persons alive, so much that it's considered a super-power. There are a lot of his speeches around, and analyses of what he does right. My favorite is this speech where you get a wonderful comparison between his opponent poor social roll, and Clinton's automatic success. Seriously, he just took 10.
Also look at some actors (e.g. Clooney, Gosling, Brosnan, Connery, Duchovny), see how they stand, how they speak, how they use their hands, how they do eye contact, and so on.
Finally, you can also look at this book, which despite its name is actually a pretty straightforward book, and widely recommended.
The best part: Practice!
Now that you've learned all that, use it! Fortunately, interacting with people is something we do way more often than waving a sword around, so you can find training situations everywhere. Learned how to smile to the barrista at Starbucks, practice to speak slowlier and louder when you're telling a story to your friends, learn how to use your hands when you're making a presentation at work, and so on.
And play social characters! Force yourself to pretend you're social, and trying to fake it until, as usual, you end up making it!
Bonus advice: don't mumble
People don't realize how soft they speak, and how counterproductive it is. Because they are so used to hearing their own voice, a lot of people grossly overestimate how loudly they are speaking, and can be barely audible without noticing it. If people often ask you to repeat what you said, speak a bit louder.