We investigate the effects of gravitational lensing in the binary pulsar system J0737Ϫ3039. Current measurement of the orbital inclination allows the millisecond pulsar (A) to pass very close (at km) in projection R ≈ 4000 min to the companion pulsar (B), with comparable to the Einstein radius (≈2600 km). For this separation at the R min conjunction, lensing causes small (about 10%) magnification of the pulsar A signal on a timescale of several seconds and displaces the pulsar image on the sky plane by about 1200 km. More importantly, lensing introduces a correction (of several microseconds) to the conventional Shapiro delay formula used in pulsar timing analysis and gives rise to a geometric time delay together with the delays associated with the pulsar spin period. These lensing effects can influence the determination of the system parameters by both timing and scintillation studies. Given the current uncertainty in the orbital inclination, more extreme manifestations of lensing (e.g., magnification by a factor of several) are possible. We compare our predictions with the existing observations and discuss the possibility of detecting gravitational lensing signatures in the system. The anomalously high point in pulsar A's light curve close to superior conjunction might be caused by gravitational lensing.