There is no such way you can create a smart collection by just specifying a month, but you can try filtering via the capture date range option and create a smart collection accordingly.
Check the below image for reference:
Please let us know if it helps.
Thanks for checking to see if there was a "month" function. I'll have to create the filter with a line for each year and then put the month in the range. Each month collection will have about 9 lines.
I would like to create a smart collection like: keyword = "chestnut-sided" and month(capture date) = august.
While you could do it with smart collections, as you observed it would be very tedious. It would be simpler to do it with the Library Filter bar. Click on Metadata and add a Date column. Expand each of the years so the months are showing. Click on August in the first year, then Cmd/Ctrl-click on August in all of the other years. Add a Keyword column to select the desired keyword(s).
If you anticipate doing this a lot, you could use the Any Filter plugin, which lets you search by month, day of month, day of week, or time of day.