We present the design and construction of an NMR probe to investigate single crystals under strain at cryogenic temperatures. The probe head incorporates a piezoelectric-based apparatus from Razorbill Instruments that enables both compressive and tensile strain tuning up to strain values on the order of 0.3% with a precision of 0.001%. $^{75}$As NMR in BaFe$_2$As$_2$ reveals large changes to the electric field gradient, and indicates that the strain is homogeneous to within 16% over the volume of the NMR coil.
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