Nowadays, an increasing amount of reclaimed asphalt pavement (RAP) is being produced from the reconstruction and/or modernisation of asphalt pavements. It is necessary to recycle the obtained RAP according to principles of sustainable development. Therefore, this work includes the design of asphalt mixtures containing RAP with bio-derived modifier and evaluates their performance properties. Crosslinked sodium alginate was applied for bitumen modification. The studies were carried out for four different modifier contents, i.e., 1.0%, 2.5%, 4.0% and 5.5%, with and without crosslinking agent. On the basis of the binder test results, the optimal amount of the additive was found to be 2.5%. The nanostructure analysis for the base and modified binders indicated a dual crosslinked biopolymer effect. As a result of the bee structure size decrease, the binder softening effect was observed. The asphalt mix properties showed that application of biopolymer-modified binder is fully justified due to the functional parameters of the mixture, especially the increased resistance to water and frost by about 9%.