A low white blood cell (WBC) count is called leukopenia. Frequent causes of leukopenia include medications (like chemotherapy), radiation therapy, immune system disease, cancers, HIV/AIDS, hypothyroidism, or severe vitamin deficiencies.
Your question is in regards to alcohol consumption and WBC count. Light to moderate consumption of alcohol should not affect WBCs. Alcoholism, when there is liver damage, can cause a low WBC due to the vitamin deficiencies and low protein that accompanies this condition. So, unless you are drinking to excess, your low WBC count is from another cause. I would recommend you see a hematologist for a full work up to find out why your count is low.