Inductance of a relay coil
A simple N channel MOSFET driving the relay will not care about the inductance - the final and full value of current the FET sees will be determined solely by the supply voltage and the coil resistance. All that the inductance can do is slow the current down a few milliseconds before it reaches the final value.

This applies whether it is a logic gate, a BJT or a switch; it's simple ohms law: -

I = V/R where V is the supply voltage and R is the coil resistance. The data sheet even tells you what this current will be so no need to do the calculation.

Make sure you use a back-emf diode though or when you open circuit the coil there will likely be a big spike of voltage (due to the inductance) that can easily damage a FET or BJT.