A rotating torsion balance method is used to detect the product of the photon mass squared and the ambient cosmic vector potential A(e). The signal is modulated by rotating the torsion balance to ensure the effectiveness of detection for all possible orientations of the vector potential. The influences of sidereal disturbances of environment are also removed by virtue of this modulation method. The experimental result shows mu(gamma)(2)A(e)<1.1x10(-11) T m/m(2), with mu(gamma)(-1) as the characteristic length associated with photon mass. If the ambient cosmic vector potential A(e) is 10(12) T m due to cluster level fields, we obtain a new upper limit on photon mass of 1.2x10(-51) g.