This analytical work focuses on enhancing the ductility capacity and damage mitigation of reinforced concrete bridge columns during earthquakes by using innovative active confinement technique. The high recovery stress associated with the shape recovery of shape memory alloys (SMAs) is exploited to apply the confining pressure. A 2-D analytical model for a single column is developed and analyzed. The model is used to evaluate the seismic behavior of the column retrofitted with SMA rings and compare it with the behavior of the column retrofitted with the more conventional approach using carbon fiber reinforced polymer (CFRP) sheets. The stress-strain behavior of the concrete confined with internal ties only, internal ties and external SMA rings, and internal ties and external CFRP sheets is described based on two different constitutive models. The column model is subjected to cyclic loading with increasing amplitude and a ground motion excitation. The analysis shows that the SMA rings provide the column with more damage protection represented by a reduction in the maximum strain by up to 273% compared to CFRP sheets. In addition, the column retrofitted with SMA rings shows smaller lateral drifts compared to the column retrofitted with the CFRP sheets when subjected to the same ground motion excitation. The superior performance of the SMA rings is primarily attributed to the increase in the compressive strength at early stages of loading associated with applying the active confinement pressure.