This study aimed to determine an optimal dosage of sunflower oil (i.e., Virgin Cooking Oil, VCO) as a rejuvenator for asphalt self-healing purposes, evaluating its effect on the chemical (carbonyl, and sulfoxide functional groups), physical (penetration, softening point, and viscosity), and rheological (dynamic shear modulus, and phase angle) properties of long-term aged (LTA) bitumen. Five concentrations of sunflower oil (VCO) were used: 1%, 2%, 3%, 4%, and 5% vol. of LTA bitumen. VCO was encapsulated in alginate biopolymer under vibrating jet technology using three biopolymer:oil (B:O) mass ratios: 1:1, 1:5, and 1:9. The physical, thermal, and mechanical properties of the capsules were studied, as well as their effect on the physical properties of dense asphalt mixtures. The main results showed that an optimal VCO content of 4% vol. restored the chemical, physical, and rheological properties of LTA bitumen to a short-term ageing (STA) level. VCO capsules with B:O ratios of 1:5 presented good thermal and mechanical stability, with high encapsulation efficiency. Depending on the B:O ratio, the VCO capsule dosage to rejuvenate LTA bitumen and asphalt mixtures varied between 5.03–15.3% wt. and 0.24–0.74% wt., respectively. Finally, the capsule morphology significantly influenced the bulk density of the asphalt mixtures.