Two large magnetic field rotations were recorded by the spacecraft Galileo 1 minute before and 2 minutes after its closest approach to the asteroid Gaspra. The timing and the geometry of the field changes suggest a connection with Gaspra, and the events can be interpreted as the result of the draping of the solar wind field around a magnetospheric obstacle. Gaspra's surface field is inferred to be within an order of magnitude of Earth's surface field, and its magnetic moment per unit mass is in the range observed for iron meteorites and highly magnetized chondrites. The location of the magnetic signatures suggests that perturbations are carried by waves in the magnetosonic-whistler mode with wavelengths between electron and ion gyro radii.