Social Security Caregiver Credit Act of 2017 This bill amends title II (Old Age, Survivors, and Disability Insurance) (OASDI) of the Social Security Act, for purposes of determining OASDI benefits, to credit individuals who serve as caregivers of dependent relatives with deemed wages for up to five years of such service. Specifically, an individual shall be deemed to have been paid a wage (according to a specified formula) during each month in which the individual was engaged for at least 80 hours in providing care to a dependent relative without monetary compensation. However, this requirement shall not apply if a larger benefit or payment would otherwise be payable. The bill also authorizes the Department of Health and Human Services to make grants to support state programs that provide medical training to individuals who provide care to dependent relatives without monetary compensation.