The superconductor Nb$_3$Sn has a high critical temperature and high critical field, widely used for high-field superconducting magnets. In this work we investigate its microscopic electronic structure with $^{93}$Nb nuclear magnetic resonance (NMR). The high-quality Nb$_3$Sn powder sample was studied in both 3.2T and 7T magnetic fields in the temperature range from 1.5K to 300K. From measurement of the spectrum and its theoretical analysis, we find evidence for anisotropy despite its cubic crystal structure. This anisotropy is manifest in alignment of powder grains under certain temperature and field cycling conditions. The Knight shift and spin-lattice relaxation rate, $T_1^{-1}$, were measured in the normal state. Additionally, $T_1^{-1}$ was measured in the superconducting state and compared with BCS theory revealing a weak field dependence, with an energy gap $\Delta(0)=2.0\pm0.08k_B T_c$ at 3.2T and $\Delta(0)=1.73\pm0.08k_B T_c$ at 7T, indicating suppression of the order parameter by magnetic field.
