The discovery in 2004 by Mars exploration rover Opportunity of sedimentary rocks with centimeter-scale trough cross-bedding is one of the compelling lines of evidence for flowing water on the Martian surface. The rocks contain a significant evaporite component mixed with weathered mafic silicates, suggesting that the aqueous fluid in contact with the sediments must have been of very high ionic strength because dissolution features are not observed. Recent thermodynamic modeling indicates that these brines could have had higher densities (by up to a factor of 1.3) and significantly higher viscosities (by up to a factor of 40) than pure water. Because fluid density and viscosity can significantly affect sediment transport mechanics, herein we analyze whether ripples could have been stable bed forms under flowing Martian brines. To this end, we compiled bed form stability diagrams with an emphasis on those studies that have considered high-viscosity fluids. For the case of viscous Martian brines, we find that ripples are stable under modest Shields numbers and low particle Reynolds numbers. These conditions translate into sediment sizes ranging from sand to gravel, and they are substantially coarser than sediment sizes for equivalent ripple-forming flows in freshwater. It is likely that ripples might also form in silt sizes under viscous brines, but these conditions (i.e., particle Reynolds numbers <0.1) have not yet been explored in flume experiments, motivating future work. Using flow-resistance equations and assuming steady uniform flow, we calculate that Marian brines must have had flow depths ranging from 0.01 to 1 m and flow velocities of 0.01 to 1 m/s, and been driven by gravity on slopes of 10^(-4) to 10^(-2) in order to generate the bed stresses necessary to produce ripples. These conditions seem reasonable given the interdune environment that has been proposed for the Burns formation. In addition to the potential for ripples in much coarser sediments, ripples formed by viscous brines also might be larger in height and wavelength than their freshwater counterparts by as much as a factor of 12. Thus, large (>.10 cm heights) and fine-grained (<1 mm particle diameter) cross strata would be compelling physical evidence for flowing brines in the Martian past, provided that independent evidence could be provided for a subaqueous (i.e., not eolian) origin of the cross-stratification. Smaller centimeter-scale ripples can also be formed by brines due to flow-depth limitations or lower-viscosity fluids, and therefore the physical sedimentological evidence in support of brines versus freshwater flows may be ambiguous in these cases.