Most of the existing studies on acid corrosion of concrete have focused on the mechanical behavior of concrete structures under monotonic load or without load. To investigate the mechanical properties of in-service concrete components under cyclic load in an acid corrosion environment, six groups of concrete prism specimens with different acid corrosion degrees (corrosion duration) were designed and prepared by the accelerated corrosion test method. The monotonic and cyclic axial compression load tests on these specimens were conducted to investigate the effects of corrosion degree on the mechanical properties of concrete specimens. The experimental results indicated that hydrochloric acid corrosion has obvious effects on the failure characteristics and mechanical properties of concrete. The surface of corroded concrete was easier to crack and spall under load, and the concrete spalling area enlarged as the acid corrosion duration increased. The compressive capacity of concrete specimens reduced rapidly with the increase in corrosion duration. The stress–strain envelope curves for concrete with different corrosion duration under cyclic load were essentially similar to that of concrete under monotonic load. The degradation rate of the descending section for the stress–strain curves of corroded concrete under cyclic load was much larger than that under the monotonic load due to the accumulation of internal damage in concrete. The peak strain and ultimate strain of corroded concrete increased significantly with the increase in corrosion duration and enhanced by 55.7% and 77.9%, respectively, compared with the uncorroded concrete, whereas the peak stress and elastic modulus rapidly decreased and reduced by 53.3% and 74.1%, respectively. Moreover, based on the strength degradation depth, the concept of effective bearing cross-sectional area ratio was proposed to characterize the corrosion degree of concrete, and the correction coefficient of descending section for the effective bearing cross-sectional area ratio was introduced to establish the constitutive model of corroded concrete under cyclic load, and the results calculated by this model matched well with the experimental values. The research in this paper can provide the experimental and theoretical basis for seismic life cycle and fatigue redesign of concrete structures in acid corrosion environments or coastal areas.