We study the dynamics of a conducting fluid carrying (i) a uniform current in the presence of a non-uniform magnetic field or (ii) carrying a non-uniform current in the presence of a uniform magnetic field, using particle image velocimetry (PIV). Our results show that the average angular velocity of the induced rotation has a power-law dependence on the electric current passing through the fluid with an exponent ≈2/3, in excellent agreement with our simulation results, for the same system. To explain the experimental observations we explore all possibilities for inducing rotation in a fluid carrying an electric current. Our theoretical discussion indicates two scenarios wherein applying electric/magnetic field on a current-carrying fluid produces rotational vortices: (i) applying a non-uniform magnetic field in the presence of an electric current and, (ii) applying a magnetic field in the presence of a non-uniform electric current. These two theoretical scenarios for inducing rotation by applying external fields agree well with our experimental observations and simulation results.