Peanut composition includes phenolic compounds, especially in the skins, which are often not consumed. High blood pressure affects more than one billion people worldwide and is considered a high-risk factor for cardiovascular diseases. Several studies have correlated antihypertensive activity with the total phenolic content present in the plants. This study evaluated the hydroethanolic extraction of phenolic compounds from the industrial residue of peanut skin and evaluated the antioxidant and antihypertensive capacity of these extracts using in vitro models. A rotational central composite design (DCCR) was proposed to study the influence of the variables: (1) the ethanol concentration on the hydroalcoholic extractor solution, and (2) the proportion of solid sample (waste) per liquid in the extraction (mass/volume) in a simple solid—a liquid extraction process. The optimal extraction conditions within this model were 50% ethanol in water, and the proportion of sample to extraction solution (m/v) equaled to 0.2. The extract obtained had significant antioxidant capacity, both in chemical (ORAC) and in cellular models, with potential for free radical scavenging. Significant levels of ACE inhibition were also found, indicating antihypertensive activity.