Acrolinx cannot process ReSt (*.rst) files directly but it could.
Solution: You could pre-process the ReSt formats and send the content to Acrolinx as HTML.
Acrolinx reads some formats directly HTML, XML, TEXT.
At the moment, we'd recommend using the Command Line Checker. You could do the pre-processing of the RST files yourselves, just as the CLC converts JSON, Properties and Java formats. This HelpCenter article may also be useful: Getting Started with Custom Integrations.
We've got an increasing number of customers deploying Acrolinx in their agile development environments. Though developers could run the command line checker manually, you can also integrate the Acrolinx checking into a build or publishing job. The result would be the URLs to the scorecards and the writers could get a notification and use the feedback to correct their texts.