Current flow through resistor in as current
Here are a couple of possible reasons the reading could be wrong:


The signal generator's output impedance is high. Some signal generators do not have a voltage-follower output buffer stage, hence while the nominal voltage of the output signal at infinite load resistance would match the actual voltage, the voltage drops significantly the moment come current is drawn from the output. Such signal generators (typically low-end or hobby class devices) require a buffer, such as a simple op-amp based voltage follower, at the output, to sustain the expected output voltage across a load.
The multimeter's current reading mode does not support AC RMS reading. Most basic multimeters fall into this category. Thus, they cannot read the AC component of current. The 0.2 mA would be the DC current component alone, i.e. some small bias current. Solution: Get a multimeter or ammeter that reads true RMS current.


To check the above possibilities, an oscilloscope would come in handy:


Measure the voltage across the resistor when the signal generator is on: Is the voltage under load actually 3 Volt RMS (8.48 Volts peak to peak for a sine wave)? Is there a DC bias or is it a true zero-centered signal?
Measure the current by using a shunt resistor in series with the load: a 1 Ohm resistor in series with the 1.173 kOhm load would develop a voltage of ~2.558 mV RMS across it, if the current were as expected. A 1 Ohm resistor is small enough in comparison to the 1.173 kOhm value to impact the results much.
Check if there is some other high resistance element in series, such as a poor connection, or oxide formation on the signal generator probes or on a breadboard contact, if you are using a breadboard.