What Resistor to use between Source and an IC
If the voltage drop across a resistor depends on it's proportion of the total resistance of the (series) circuit, then shouldn't I need to have the resistance of the IC?


Exactly right and since the "resistance" of the IC varies with whatever it is doing the resultant voltage to the IC would vary too. That's why we don't regulate voltage in this manner.

Instead, you require a regulated power supply which will hold the output voltage steady across a wide range of currents. The chip you have chosen has a 2 to 6 V operating range but 5 V would be standard and a suitable ready-made PSU such as USB chargers are readily available and provide the voltage regulation you require.