We derive a simple formula which gives the general relativistic deflection of a spacecraft, idealized as a point mass, for all values of the asymptotic speed V(infinity) (0< or =V(infinity)< or =1). Using this formula we suggest a new test of general relativity (GR) which can be carried out during a proposed interstellar mission that involves a close pass of the Sun. We show that, with foreseeable improvements in spacecraft tracking sensitivity, the deflection of a spacecraft's trajectory in the gravitational field of the Sun could provide a new test of GR.