In this paper, a compact, high efficiency, adjustable fiber optic true time delay (TTD) line for fast steering phase array antenna beam is proposed. The key features of this approach are: (1) sub-ps time resolution (< 0.5 ps) so that high accuracy TTD can be achieved for tens of GHz antenna signals; (2) large number of TTD channels (> 1000) can be addressed due to the tunable nature of our unique electro-optic grating material. An analysis on component parameter selection and system performance are provided.