The effects of a random current on the fluctuations of underwater cw sound transmissions are considered for a horizontal isospeed channel. A statistical ensemble of currents is employed, whose members are depth dependent only, and current influence on ray geometry is investigated. Approximations to the total acoustic field at a receiving point are obtained, and it is shown that a current ensemble member has a significant effect on phase. A mean current is taken, on which are superimposed small depth‐dependent current changes in speed and direction. These changes are members of statistical ensembles, which lead to an ensemble of phase functions. Expressions for the mean and standard deviation of the phase, in terms of statistics of the depth‐averaged current fluctuations, are determined and analyzed. The inverse problem of determining second‐order moments of the random current, given the standard deviation of phase, is examined also. If the mean current is known, phase information at three receivers is sufficient to specify the second moments of the current fluctuations.