I am designing a circuit whose output I have attached (Amplitude is 100mV and Frequency is 20kHz). I want to shift this output to 0.5 V DC level. I will be thankful if anybody could suggest me a DC level shifter for this scenario.(Particularly I am looking for a mosfet based circuit.)
Your output looks as a analog signal so add a simple summing amplifer with 2 input voltages. The first input voltage should be the output voltage which you have shown. The second should be the constant 0.5 Volt.
Just add 2 resistors. If the AC source amplitude is Vac and you want to add 0.5V, first determine a DC supply value, say 5V.
Just as BradtheRad says, a voltage divider between two voltage sources will generate a summing of both signals with some attenuation. To supress that total AC attenuation you must amplify it before the divider.
Another option: AC couple with a cap, then shift to whatever voltage you want. Unless it's very slow this is quite easy, and won't attenuate (<<1%) with proper component selection. But it will have some start up time and won't work for DC.