The water supply valve on my toilet is leaking right at the knob to turn the water on/off.
Can I fix this or do I need a plumber?

You can tighted the packing nutthe nut behind the handle

James's correct. The bonnet packing nut's located on the stem just under the handle. Close the valve and open it up a bit until it starts to leak. Now snug up the bonnet packing nut until the leak stops. DO NOT OVERTIGHEN!!
Good luck, Tom