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% by mass of whole 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 containing a (meth)acrylic acid alkyl ester having 7-17 carbon atoms and a weakly basic monomer; and a medical patch containing an adhesive composition containing a salt of a basic drug and the star-shaped acrylic block polymer as an adhesive that exhibits high drug efficacy, that does not cause a decrease in adhesive property of an adhesive base due to an additive, and that causes less skin irritation.