The frequency-independent rms temperature fluctuations determined from the COBE-DMR two-year sky maps are used to infer the parameter Q(rms-PS), which characterizes the normalization of power-law models of primordial cosmological temperature anisotropy, for a forced fit to a scale-invariant Harrison-Zel'dovich (n = 1) spectral model. Using a joint analysis of the 7 degrees and 10 degrees ''cross''-rms derived from both the 53 and 90 GHz sky maps, we find Q(rms-PS) = 17.0-(+2.5)(2.1) mu K when the low quadrupole is included, and Q(rms-PS) = 19.4(+2.1)(+2.3) mu K excluding the quadrupole. These results are consistent with the n = 1 fits from more sensitive methods. The effect of the low quadrupole derived from the COBE-DMR data on the inferred Q(rms-PS) normalization is investigated. A bias to lower Q(rms-PS) is found when the quadrupole is included. The higher normalization for a forced n = 1 fit is then favored by the cross-rms technique.