I service in the military from 1964 to 1968. Can I get credit on my social security for this.
What you could get from Social Security are deemed military wages (DMW) for your periods of active US military service (https://www.ssa.gov/OP_Home/handbook/handbook.09/handbook-0953.html). These 'extra' wages would then added to your actual wages when calculating your Social Security retirement benefit rate.
DMWs are automatically added for years after 1967, but you normally must submit proof of your periods of active duty (e.g. form DD-214) for earlier years. If you haven't yet filed for benefits you should plan on submitting proof of your service to Social Security when you do. Or, if you're already receiving benefits and you don't know if you were credited for your service, you could check with Social Security or submit proof of your service and request a recalculation of your benefit rate.