i dont know, there is a small whole in the handle, but i dont know how to remove the screw there
you would need an allen wrench otherwise known as a hex key.
turn off the water under the sink and remove the handle and take apart the stem assembly. if the stem looks like this then it is moen and you will need to contact moen for replacement parts. the parts will most likely be free. 1800buymoen.
if there is a ball and under that there is a spring and rubber bonnet then it is a delta brand. replace those springs and washers and that will repair it. they are available at any hardware store.