The orthogonal array design method was used to optimize ultrasonic-assisted extraction of resveratrol from peanut sprouts. The results showed that the highest extraction yield of resveratrol using ultrasonic-assisted extraction could be up to 1.1%. The optimal extraction conditions were liquid to solid ratio of 30:1 (mL/g) and ethanol concentration of 80% (v/v) as solvent for 40 min at the temperature of 70 °C. AB-8 macroporous adsorption resin was used to purify the crude extract and the resveratrol content increased to 47.5% after one treatment run. The optimal adsorption parameters were initial concentrations in the sample solution of 2 mg/mL, a pH of 5.0, a flow rate of 2 mL/min, and a temperature of 25 °C. The optimal desorption parameters were 60% ethanol and a flow rate of 1 mL/min. The chemical composition of the peanut sprout’s resveratrol sample was investigated via HPLC, and the predominant constituents were found to be protocatechuic acid, catechins, caffeic acid, epicatechuic acid, resveratrol, and rutin. The antioxidant activities of the resveratrol were measured via the following different analytical methods: reducing power, 2,2-diphenyl-1-picrylhdrazyl (DPPH), hydroxyl radical-scavenger activity, superoxide radical-scavenger activity, the β-carotene bleaching test, and the scavenging nitrite test. The results indicated that the resveratrol in peanut sprouts have significant antioxidant activities and can be used as a source of potential antioxidant. And peanut sprout’s resveratrol has the potential and valuable application to be used as a new type of resveratrol resource. The finding of this study can provide some theoretical reference for the comprehensive utilization of peanut resources in the development of antioxidant health foods.