I'd probably recommend Tai Chi over karate, but you should try out different styles and see if anything "clicks" with him. If he is reluctant, show him the recent remake of the Karate Kid. I'd imagine he would be able to identify with the protagonist, and it might motivate him, as it has enough "violence" to appeal to him, but the message of the movie doesn't glorify violence and if it can get him to want to learn from a good instructor it will help him.
I wouldn't worry too much about the violence aspect yet. Kids go through stages and as long as you can channel his obsession with violence into healthier outlets you shouldn't need to worry. My son is currently obsessed with WWII and soldiers and Nazism and has decided he wants to go into the military. That got started because we started watching Hogan's Heroes, so his idea of what war and Nazis are is decidedly unrealistic.
Most of my nieces and nephews went through "we wanna hit each other with sticks" phases, inspired by Star Wars and anime movies. My husband, who has had a lot of fencing and bokken training would take them out in the back yard with 3-foot lengths of PVC pipe wrapped with thick insulation and duct tape, and teach them the mechanics of sword fighting, including lessons on safety and sportsmanship.
If he is being bullied at school, of course he is going to fantasize about a world where he is strong and tough and in control. This is normal, and is no unhealthier than a world where kids are bullied and have no advocates in the teachers who should be looking out for that. I'm sorry your son's school isn't doing a better job. The school my kids went to was outstanding in that regard. Zero tolerance for intolerance, and "bully awareness" in every grade. I took every opportunity I could to tell them how much I appreciated the job they were doing. Both my husband and I suffered a great deal of bullying in our childhoods because the schools were either ignorant or indifferent to the problem, and we are both so grateful that our children are being spared that.
What may make the difference between raising a child whose personality develops in reaction to being bullied (and we've all seen the possible results of that, plastered all over the media), and one who has a healthier perspective, is what steps you take to give your son the opportunity to control his environment as it affects him in regard to violence and other threats.
Talk to his teachers, maybe they will be able to make changes that will make him feel safer. If it were me I'd start with the principal and ask him what measures were in place to deal with bullying in school. If he has a good answer, make sure your son knows what help is available to him. If there is nothing in place to help him, raise h**l. You are, and must be, your son's greatest advocate. There is no excuse for a school which doesn't address this issue. None.
Training in martial arts can also be a game changer. As long as you get a good instructor. If you haven't seen the Karate Kid (2010 version) I'd recommend it...it has some great examples of both good and bad instructors. Exaggerated of course, but you have to exaggerate a bit with kids :)
Aside from the self discipline and physical and martial training, one benefit kids can get from martial training is that it reduces the trauma of physical violence. Children who grow up tussling with their siblings have healthier attitudes about and reactions to physical conflicts. There's a good article about that here: http://www.todaysparent.com/family/parenting/roughhousing-aggressive-or-constructive-behaviour/
If kids don't have access to that kind or outlet, martial arts may supply an alternative.