Cover crops can improve soil health by maintaining soil organic carbon (SOC) and nitrogen (N) contents, yet their dynamics in relation to crop yield in a semi-arid cropping system are poorly understood. The main objective of this study was to evaluate the response of diverse winter cover crop species and their mixture on SOC and N fractions and their relationship with sorghum (Sorghum bicolor L. Moench) yield in a winter wheat (Triticum aestivum L.)–sorghum–fallow rotation with limited irrigation management. Cover cropping treatments included pea (Pisum sativum L.), oat (Avena sativa L.), canola (Brassica napus L.), and mixtures of pea+oat (POM), pea+canola (PCM), peat+oat+canola (POCM), and a six-species mixture (SSM) of pea+oat+canola+hairy vetch (Vicia villosa Roth)+forage radish (Raphanussativus L.)+barley (Hordeum vulgare L.) as cover crops and a fallow. Soil samples were analyzed for residual inorganic N, potentially mineralizable carbon (PMC) and nitrogen (PMN), SOC, and total N. Response of labile inorganic N, PMC, and PMN varied with cover crop treatments. The SOC and total N contents did not differ among treatments but were 20% and 35% higher in 2020 than in 2019, respectively. Sorghum grain yield was 25% and 40% greater with oats than with PCM and canola cover crops in 2019, while it was 33–97% greater with fallow and oats than other treatments in 2020. Oat as a cover crop could improve the resilience of limited-irrigation cropping systems by increasing SOC, soil N, and crop yield in semi-arid regions.