Agar, a naturally occurring polysaccharide, has been modified by grafting it with acrylic (AcA) and methacrylic (McA) acid monomers, resulting in acrylic or methacrylic acid grafted polymer (AA-g-AcA or AA-g-McA) with pH-sensitive swelling behavior. Different ratios between agar, monomers, and initiator were applied. The synthesized grades of both new polymer series were characterized using FTIR spectroscopy, NMR, TGA, DSC, and XRD to ascertain the intended grafting. The percentage of grafting (% G), grafting efficiency (% GE), and % conversion (% C) were calculated, and models with optimal characteristics were further characterized. The swelling behavior of the newly synthesized polymers was studied over time and in solutions with different pH. These polymers were subsequently crosslinked with varying amounts of glutaraldehyde to obtain 5-fluorouracil-loaded nanogels. The optimal ratios of polymer, drug, and crosslinker resulted in nearly 80% loading efficiency. The performed physicochemical characterization (TEM and DLS) showed spherical nanogels with nanometer sizes (105.7–250 nm), negative zeta potentials, and narrow size distributions. According to FTIR analysis, 5-fluorouracil was physically incorporated. The swelling and release behavior of the prepared nanogels was pH-sensitive, favoring the delivery of the chemotherapeutic to tumor cells. The biocompatibility of the proposed nanocarrier was proven using an in vitro hemolysis assay.