Can I deduct the mileage cost for driving a parent to medical appointments? (Parent does not live with me.)

[Coleen3]

Only if they are your dependent.

Whose Medical Expenses Can You Include? 

You can generally include medical expenses you pay for yourself, as well as those you pay for someone who was your spouse or your dependent either when the services were provided or when you paid for them. There are different rules for decedents and for individuals who are the subject of multiple support agreements. See Support claimed under a multiple support agreement, later, under Qualifying Relative. 

https://www.irs.gov/pub/irs-pdf/p502.pdf