  We report on the measurement of the contribution of the magnetic-dipole
hyperfine interaction to the tensor polarizability of the electronic
ground-state in $^{87}$Rb. This contribution was isolated by measuring the
differential shift of the clock transition frequency in $^{87}$Rb atoms that
were optically trapped in the focus of an intense CO$_2$ laser beam. By
comparing to previous tensor polarizability measurements in $^{87}$Rb, the
contribution of the interaction with the nuclear electric-quadrupole moment was
isolated as well. Our measurement will enable better estimation of black-body
shifts in Rb atomic clocks. The methods reported here are applicable for future
spectroscopic studies of atoms and molecules under strong quasi-static fields.
