The Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) onboard the Mars Express spacecraft has occasionally displayed surprising features. One such feature is the occurrence of a series of broadband, low-frequency echoes at equally spaced delay times after the sounder transmitter pulse. The interval between the echoes has been shown to be at the cyclotron period of electrons orbiting in the local magnetic field. The electrons are believed to be accelerated by the large voltages applied to the antenna by the sounder transmitter. Measurements of the period of these “electron cyclotron echoes” provide a simple technique for determining the magnitude of the magnetic field near the spacecraft. These measurements are particularly useful because Mars Express carries no magnetometer, so this is the only method available for measuring the magnetic field magnitude. Using this technique, results are presented showing the large scale structure of the draped field inside the magnetic pile-up boundary. The magnitude of the draped field is shown to vary from about 40 nT at a solar zenith angle of about 25°, to about 25 nT at a solar zenith angle of 90°. The results compare favorably with similar results from the Mars Global Surveyor spacecraft. A fitting technique is developed to derive the vector direction and magnitude of the draped magnetic field in cases where the spacecraft passes through regions with significant variation in the crustal field. The magnetic field directions are consistent with current knowledge of the draping geometry of the magnetic field around Mars.