ABSTRACT Long-term studies of binary millisecond pulsars (MSPs) provide precise tests of strong-field gravity, and can be used to measure neutron-star masses. PSR J1909-3744, a binary MSP has been the subject of several pulsar timing analyses. The edge-on orbit enables measurement of its mass using the Shapiro delay; however, there is degeneracy in the sense of the inclination angle, i, and multiple solutions for the longitude of ascending node, Ω. Radio pulsars scintillate due to inhomogeneities in the ionized interstellar medium (IISM). This can result in scintillation arcs in the power spectrum of the dynamic spectrum that can use these to study the interstellar medium and constrain binary pulsar orbits. Here, we study the scintillation of PSR J1909-3744 using observations from the 64-m Parkes Radio Telescope (Murriyang) over ≈13 yr, using techniques to study scintillation in a lower signal-to-noise regime. By monitoring annual and orbital variations of the arc-curvature measurements, we are able to characterize the velocity of the IISM. We find that the statistics of the IISM remained stationary over this time and a slightly anisotropic model (axial ratio ≳1.2) is preferred. We measure the relative distance to a single dominant thin scattering screen at s = 0.49 ± 0.04, or Ds = 590 ± 50 pc, with an angle of anisotropy ζ = 85 ± 6° (East of North) and velocity in the direction of anisotropy VIISM,ζ = 14 ± 10 km s−1. By combining a physical model of the IISM and current pulsar timing results, we also constrain Ω = 225 ± 3° and i = 86.46 ± 0.05°.