Connecting a single resistor to a power rail will change its current.
If you connect a resistor between high and low voltage, creating a complete circuit, the applied voltage will induce current. Is this what you mean by 'change its current'?
If I checked the voltage before and after the resistor, it would stay the same.
This implies one of two things:
- You don't have a complete circuit, or
- If you do have a complete circuit, there's another resistance in series that's orders of magnitude higher than the resistor you're measuring across.
Simplisticly, this SRAM IC most likely has open-collector outputs. The data lines are connected to switches which are closed when a logic 0 is desired (pulling the pin to ground) or open (superhigh impedance) when a logic 1 is desired.
So, if the data line is open, the circuit isn't complete (there's no path through the open collector output), there isn't any current, and by Ohm's law, no voltage drop across the resistor.
How then, is this dropping the voltage?
If the SRAM changes the output to zero, you'll ideally have a (VCC - GND) volt drop across the resistor. (In reality, the switch won't be a dead short, and will have a few ohms of resistance). The purpose of the resistor isn't to drop the voltage per se, it's to limit the current to an acceptable amount so that when the open-collector output pulls the signal low, it doesn't fry due to excess power dissipation.