While software and algorithms have become increasingly important in astronomy, the majority of authors who publish computational astronomy research do not share the source code they develop, making it difficult to replicate and reuse the work. In this paper we discuss the importance of sharing scientific source code with the entire astrophysics community, and propose that journals require authors to make their code publicly available when a paper is published. That is, we suggest that a paper that involves a computer program not be accepted for publication unless the source code becomes publicly available. The adoption of such a policy by editors, editorial boards, and reviewers will improve the ability to replicate scientific results, and will also make the computational astronomy methods more available to other researchers who wish to apply them to their data.