YOU can't.
But the Karate and science summer camp are GREAT ideas.
Karate is an individual sport. My kids both do it...ours son since before he was 6 yrs old. He is working on his 2nd degree Black belt right now. It can be a wonderful self-esteem builder. Most (be sure to visit classes and see for yourself though) schools' instructors are very cognizant of helping build self esteem in the kids. They expect respect from them, and they show respect to them. Respect is a HUGE deal in martial arts. And it includes respecting YOURSELF. Getting involved with martial arts can also help your son gain some possibly lacking self-confidence. That can go a long way with bullying issues.
The science camp will expose him to other like-minded kids. He may even meet/make a great new best friend. Maybe even someone else who is experiencing or has experienced the sort of social issues your son is dealing with.
Also, if he is 10, then he is probably going into 6th grade next year... right? Our school has 6th grade as the first year of middle school. So you have several schools that feed into that one middle school.... and TONS of new kids. In fact... ALL the 6th graders will be "new". So it is a whole new year with a LOT of new kids for him to "start over" with. It can be challenging when they transition (change classes for every subject, the sheer numbers of students, and going from being the biggest to the smallest on campus), but it is also full of opportunity for him.
Also, if he does meet some new kids at science camp, try to invite them to do something together... an afternoon at the movies or playing putt putt or SOMEthing to help facilitate a friendship.
My son (7th grade this year) was never that sports minded either. But having lots of friends in other venues than school (karate, church, his former private school friends, extended family, friends in the neighborhood) really helped keep him balanced if things were rough AT school.
hth