The present invention provides: a star-shaped acrylic block polymer having a star-shaped structure in which at least three chain polymer portions radiate from a mercapto group situated at the center, wherein (meth)acrylic acid alkyl ester structural units having 7-17 carbon atoms account for 30-99.9 mass% of all structural units of the star-shaped acrylic block polymer, and at least one of the chain polymer portions has a copolymer structure of polymerizable monomers including a weak basic monomer and (meth)acrylic acid alkyl ester having 7-17 carbon atoms ； and a medical adhesive patch that exhibits high efficacy, that causes less skin irritation and does not cause a decrease in adhesive properties of the adhesive base due to additives, and that contains a salt of a basic drug and an adhesive agent composition containing the star-shaped acrylic block polymer as an adhesive agent.
