The homology of a differential graded algebra has an $A_\infty$-algebra structure which is unique up to non-unique isomorphism.
See Keller's nice expository paper, for instance. In particular, he states this result in Section 3.3 (as a theorem due to Kadeishvili, among others). It is stated there as a result about the homology of an $A_\infty$-algebra, but any differential graded algebra may be viewed as an $A_\infty$-algebra.
