Viscosity is an inherent characteristic of fluids and is therefore an important parameter in many different processes. Current methods to measure viscosity involve direct contact with the liquid sample, which is often undesirable. Here we present a simple, precise and robust contact-free method to determine viscosity, using a single drive motor, inexpensive components and disposable sample vessels. The measurement principle involves the detection of viscosity-dependent angular positions in a rotating liquid relative to the direction of centrifugal acceleration in an orbitally shaken vessel. The signal can be detected using different optical methods, as shown here using fluorescence and transmitted light. The sensitivity of the system can be adjusted over a wide range by varying the sample volume or the shaking diameter, and multiple samples can be analysed in parallel. This novel viscometer is also applicable to characterize non-Newtonian shear rate-dependent fluids.