Hey,
I want to determine the phase difference between 2 burst of square waves (100 cycles) of 550kHz. Can I feed this wave to MSP430g2553 and measure it? is there a register to store these waves to be analyzed?

the difference in the phase is what I am interested in

 

Sure it is possible. There is no need to store the waves.
Use the input capture feature of the timer module and measure the time difference between edges of the square waves.