To achieve common goals, we often use joint commitments. Our commitment helps us to coordinate with our partners and assures them that their cooperative efforts will benefit themselves. However, if one of us can exploit the other's cooperation (as in the Prisoner's Dilemma), our commitment appears less useful. It cannot remove the temptation for our partners to exploit us. Using methods from evolutionary game theory, we study the function of joint commitments in the Prisoner's Dilemma. We propose a reputation system akin to indirect reciprocity, wherein agents observe interactions even when not directly involved. They judge cooperation as good and defection as bad, but, crucially, only if the parties involved had committed to cooperate. This results in stable cooperation even though judgments are made privately, which had been a weakness in previous models of indirect reciprocity. Our work shows that joint commitments have utility beyond coordination problems, which could explain their prevalence. The proposed link between joint commitments and reputation could also explain why some joint commitments are pointedly public, like wedding vows. A reputation-based mechanism might have been particularly relevant in our distant past, in which no institutions existed to enforce commitments.