Phage therapy, i.e., the treatment of chronic bacterial infections by virus that kill bacteria has shown promise in combating antimicrobial resistance (AMR). A typical phage particle is around 100 times bigger than a typical antibiotic molecule. Due to larger size, a phage particle diffuses slower than an antibiotic molecule, and can get trapped in the polymeric mesh of biofilm matrix. We report that a swarm of Capnocytophaga gingivalis, a bacterium abundant in the human oral microbiota, can actively transport phages over long distances. By tracking fluorescently labeled lambda phages that do not infect C. gingivalis, we demonstrate active predator transport by a C. gingivalis swarm. As a result, the rate of disruption of the prey, i.e., an Escherichia coli colony increases 10 times. Production of curli fiber by a mature E. coli biofilm blocks the intercellular space and is known to inhibit the diffusion of phages within a biofilm. We find that C. gingivalis forms tunnels within the prey biofilm. When phages are actively delivered, curli fiber containing E. coli biofilms are no longer protected against phage infection. Our results demonstrate that active delivery of the predator by a self-propelled swarm might improve the pharmacokinetics of phage therapy. This can lead to the development of a tool to combat chronic AMR biofilms.