We report on the construction of a two-axis goniometer intended for low-temperature, single-crystal nuclear magnetic resonance (NMR) measurements. With the use of home-made and commercially available parts, our simple probe-head design achieves good sensitivity, while maintaining a high angular precision and the ability to orient samples also when cooled to liquid helium temperatures. The probe with the goniometer is adapted to be inserted into a commercial ⁴He-flow cryostat, which fits into a wide-bore superconducting solenoid magnet. Selected examples of NMR measurements illustrate the operation of the device.