I think you would need a datasheet of the motor with its electrical and mechanical characteristcs to determine the current. But that would still be a theoretical value. In the real world you will have the wires, contacts and so on, that add additional resistance and will "help" to limit the start current. But don't choose the wires to small and use a fuse for safety reasons. This should help you to choose the right wires: American Wire Gauge
If it's a DC motor there is a better and quiet simple solution.
Because of mechanical wearing and the limited switching frequency you should better not use a relay. The better solution would be an application fitting field effect transistor (FET)switching at a pwm frequency of about 20kHz so it would not produce any annoying humming or whimpering sounds in the motor. Depending on the transistor you will need a driver circuit for the FET to operate fine, dropping just a small ammount of power (passive cooling might still be needed).
For a smooth start of the motor with a minimum of peak current you should apply a linear duty cycle sweep from 0 to 100%. The optimum duration of the sweep depends on the motor and the mechanical load. Discover your optimum by trying different sweep durations.