It sounds like the packing in the valve stem assembly is leaking.
There should be a nut at the top of stem before the handle. This nut may be loose and need tightning. Tightning the nut will tighten the packing around the stem. Do not over tighten as it will make it difficult to turn the valve to open it. Probably 1/8 to 1/4 turn will be enough.
Good Luck!