A new, to the best of our knowledge, scalar quantity characterizing radial correlations among all the orbital angular momentum (OAM) modes present in a random beam is introduced. It is given by the maximum value of the interference fringe contrasts produced by the filtered pairs of the OAM modes. This new measure is termed the OAM degree of coherence (DOC) in similarity with the electromagnetic (EM) degree of coherence which describes two-point correlations in polarization components of the electric field. The theoretical development is augmented by several numerical examples. Moreover, the possibility of combining the OAM and the EM degrees of coherence in one quantity is also outlined.