Do you have an aspirin ? Do you have any aspirin ? Either is acceptable

If this is a grammar exercise, I suspect your teacher is looking for 'any'. In the sentence 'Do you have any aspirin?', this is an uncountable noun, referring to the substance/drug compound in general terms. You might ask this in a shop, for example, when you want a whole bottle or packet. But 'aspirin' is also used as a countable noun, referring to the tablets themselves. For example, you could buy a packet of 24 aspirins - this is countable. So, if you have a headache and you want to know if your friend has one tablet in her handbag that she can give you, you might say 'Do you have an aspirin?'