Q: Is there a way to add keywords to a published paper?
Keywords are meant to improve the searchability of your paper – to increase the chances of your paper being displayed in a search by relevant readers. However, there are other elements of a paper that also serve to do this, including the title and the abstract. While the title is typically not meant to include all the keywords, it does contain other words and terms integral to the research. The abstract, in providing a gist of the paper, also tends to include essential words and terms from the paper, and these are also assessed by the search engine in delivering the result.
By your question, I understand that your paper already has some keywords and that you wish to include a few more to enhance its searchability. If so, note that the present keywords have already been reviewed and determined as appropriate and sufficient for this purpose. Additionally, the journal may have a cap on the number of keywords you can include for a paper. Finally, databases such as PubMed have their own system of indexing an article (known as medical subject headings, or MeSh) for delivering search results, which does not really depend on keywords.
If you have already used an effective strategy in choosing the keywords for your paper (such as described in this resource), you should be fine. Nevertheless, if you wish, you may go ahead and write to the editor about this. As this is a relatively minor request, not affecting the science of the paper, and easily executable, they may agree to your request. However, for the very same reasons, they may not, or at least, not treat this with utmost urgency. This would entirely depend on the journal.