We report a dramatic orbital modulation in the scintillation timescale of the relativistic binary pulsar J1141--6545 that both confirms the validity of the scintillation speed methodology and enables us to derive important physical parameters. We have determined the space velocity, the orbital inclination and even the longitude of periastron of the binary system, which we find to be in good agreement with that obtained from pulse timing measurements. Our data permit two equally-significant physical interpretations of the system. The system is either an edge-on binary with a high space velocity ($∼ 115$ km s$^{-1}$) or is more face-on with a much slower velocity ($∼ 45$ km s$^{-1}$). We favor the former, as it is more consistent with pulse timing and the distribution of known neutron star masses. Under this assumption, the runaway velocity of 115 km s$^{-1}$ is much greater than is expected if pulsars do not receive a natal kick at birth. The derived inclination of the binary system is (76± 2.5^{∘}) degrees, implying a companion mass of 1.01 (± )~0.02 M(_{⊙}) and a pulsar mass of 1.29 (±)~0.02 M(_{⊙}). Our derived physical parameters indicate that this pulsar should prove to be an excellent laboratory for tests of gravitational wave emission. Comment: Minor text and figure changes and corrections following referee's Comments. 14 pages, 3 figures, accepted for publication in ApJ