I've just started robotics and ROS and I wondering if I can control a DIY Robot Arm Kit Educational Robotic Claw Set (I think its motherboard is arduino).
You can find the kit here.
Can I use ROS to control such kind of kits?
The answer is a resounding 'yes'. Check out this ROS package here.
You'd have to get a little creative with your code to control all of your servos, but I think you're good to go.
the answer for this kit is most likely yes, has it has standards servos and arduino board so the drivers already exit.
ROS can be used with arduino board with the rosserial package, which contains a library for servos.
You will need to update the code on your arduino accordingly to your need in order to be able to have control over ROS on a remote machine.