What have you tried so far?
(Assuming its not against their terms & conditions)
I don't see any sort of feed for issues, so you'll have to do some magic yourself.
From a quick look at the site it seems that the issues have a url like http://www.themagpi.com/issue/issue-19/pdf/
The number increments with each issue, so first of all you need some sort of script to increment the number based on the month. Then you can wget that into your local dir. Monthly activity can be scheduled via cron.
A simple google search on dropbox raspberry pi turned up this http://www.raspberrypi.org/phpBB3/viewt ... 30&t=21617
Tie it together, and away you go.