The Weather Underground site has data from a network of unofficial weather stations, and you can enter a location and then select one of those stations, including two in/near two stations in or near Davis Square.
From there, you can get daily, weekly, and monthly weather data; those two are reporting 6.75 and 7.19 inches of rain, respectively, so far this month. For June 2023, they give me either 6.47 or 5.95 inches of rain.
Those don't give past years or averages; The site teddywolf found might be better for that; the NWS/NOAA sites have historical data, and may be better calibrated than the hobbyist Weather Underground local weather stations.
some current Somervillle numbers
From there, you can get daily, weekly, and monthly weather data; those two are reporting 6.75 and 7.19 inches of rain, respectively, so far this month. For June 2023, they give me either 6.47 or 5.95 inches of rain.
Those don't give past years or averages; The site