Hi @nels,
There is a way without using a raspberry pi. It is not simple unless some one writes some code for you. There is an IFTTT app which you can select to record your data to google sheets. It will record a new row every minute even without you running a computer. But the major problem is that every 2000 rows (usually 2000 minutes) it starts writing to a new spreadsheet. I have not heard of anyone on this forum bothering to write some code to solve that issue. I decided to go the raspberry pi method thanks to @GaryFunk.
A solution for you would be to find some one to write some code for you which runs every time a new row is added to the google sheet, that reads the new row and adds the rainfall to your monthly total on a monthly rainfall sheet, and deletes a row from the original sheet so that it never exceeds 2000 rows.
The Google sheets discussion is here: Including Sky data into Google Spreadsheet
cheers Ian 