What are the professional options for publishing research software?

Using a software repository (see http://software.ac.uk/resources/guides/choosing-repository-your-software-project). GitHub is often used for this purpose. You can also connect DOIs to versions of your software on Github and Zenodo. This makes identification and citation easier.
Publish in a software journal (see http://software.ac.uk/resources/guides/which-journals-should-i-publish-my-software)
Small programs consisting of only a few lines of code can be added to your research data as a text file.