I have a sensor which is connected to +12V and it shows some small variations at the output.
I have an opamp which I have configured in AC input, inverting amplifier. therefore I should supply it with the load voltage and then find the best value for + rail (by default the half of the VCC which is 6V), something like the figure below, but the opamp maximum supply is 3.3V. I am bounded to use this opamp and I can not change the sensor voltage.
You don't mention what opamp you're using?, is it rated for use at 3.3V? (which sounds extremely low), you probably need to find one that will work from such a low voltage.