Here is an easy to use meteorological drought monitoring software (MDM). Apart from SPI, it also enables you to calculate several other indices including: deciles index, Percent of Normal Index, Rainfall Anomaly Index, effective drought index, China-Z index, modified CZI, and Z-Score Index. Your calculations can be annual, seasonal, monthly and moving averages for 3, 6, 9, 12, 18, 24, 48 months. I hope this helps!
You need to click on the right corner on the "download" button. There is also a manual on how to use it on the same website.
You can calculate SPI from daily, weekly and monthly rainfall data. You can try to select a twelve-months moving average window computation. The SPI model will generate monthly SPIs over a selected time-series input data.
There is several tool for calculating SPI. I compared three of them and I found the tool of mitigation drought center(the above link) is same as MDM(the above link). you can read the result on my website. I can't put the link of my website here but you can find the page related to this matter by search "drainc spi gamma distribution" in google.