We present here an experimental, strictly one-dimensional rotational system, made by using single magnetic Janus particles in a static magnetic field. These particles were half-coated with a thin metallic film, and by turning on a properly oriented external static magnetic field, we monitor the rotational Brownian motion of single particles, in solution, around the desired axis. Bright-field microscopy imaging provides information on the particle orientation as a function of time. Rotational diffusion coefficients are derived for one-dimensional rotational diffusion, both for a single rotating particle and for a cluster of four such particles. Over the studied time domain, up to 10 s, the variation of the angle of rotation is strictly Brownian; its probability distribution function is Gaussian, and the mean squared angular displacement is linear in time, as expected for free diffusion. Values for the rotational diffusion coefficients were also determined. Monte Carlo and hydrodynamic simulations agree well with the experimental results.