Tearing mode stability analysis in the presence of circulating energetic ions (CEI) is studied in the reversed field pinch (RFP) magnetic configuration. In contrast to the minimal effect of precessional drift of CEI on tearing modes in tokamaks, the effect of precessional drift of CEI on tearing modes is important in the RFP. It is found that the effects of CEI on tearing modes in RFP depend on their toroidal circulating direction, and have a strong relation to the pressure gradient of CEI. For co-CEI, tearing modes can be stabilized if the pressure gradient of energetic ions is sufficiently large, which is qualitatively consistent with experimental results in the Madison Symmetric Torus.