Carrot (Daucus carota L.) is one of the main root vegetables rich in bioactive compounds with appreciable health-promoting properties, largely consumed in Algeria. In the current study, the storage effect (at 4 °C throughout 12 days) on bioactive compound stability and the antioxidant activity of two Algerian orange carrot varieties (Supermuscade and Touchon) were investigated. Total phenolic content of samples was determined by the Folin–Ciocâlteu method. Antioxidant capacity was determined spectrophotometrically, based on the evaluation of Free Radical Scavenging Activity (FRSA) using DPPH radical and Ferric Reducing Power (FRP). The results showed that the Touchon variety is richer in phenolics, flavonoids, and carotenoids and presents higher antioxidant activity in comparison with the Supermuscade variety. At the end of storage, the bioactive compound content and antiradical activity increased significantly (p < 0.05). Also, an extremely significant correlation (p < 0.001) was observed between the antioxidant contents and the antioxidant capacities of aqueous carrot extracts.