In this paper, we study the gravitational deflection of light by a Janise-Newman-Winicour (JNW) wormhole in the weak-field limit. Based on the harmonic gauge, we first derive the exact metric of the JNW wormhole in harmonic coordinates. Moreover, using the geometric method proposed by Gibbons and Werner, we apply the Gauss-Bonnet theorem to the optical metric of this gravity, and obtain the analytical form of the equatorial gravitational deflection angle of light up to the third order induced by the JNW wormhole. For the Schwarzschild geometry, the resulting bending angle is consistent with that of the results obtained by the method in the framework of general relativity.
