I need a sinusoidal varying capacitor to test a differential capacitance circuit. I will use the circuit to test MEMS gyroscope/accelerometer capacitance change. But right now I do not have the gyroscope/accelerometer prototype. Is there any available chip or method by which capacitance can be change by varying the input voltage by function generator.
This is what a varactor diode does. The width of the depletion layer changes with applied reverse voltage. This changes the capacitance seen by small signal relative to the DC offset.
Such diodes used to be popular for fine-tuning radio receivers, the resonance of crystal oscillators, etc.
If the bias voltage change won't bleed through too much you can use a varactor or indeed any reverse-biased diode. It's preferable to use two varactors back-to-back so that nonlinearities cancel out to a first order (for the signal, not the bias).
If you need very small or very large capacitance you may have to use a part that is not designed as a varactor.
You might want to consider a motor driving an air dielectric capacitor. Keep the separation constant and change the overlap between the plates like an old-school tuning capacitor. Keeping it sinusoidal would be an interesting field solver project.