This can be achieved using the smooth cumulative
option when plotting:
set xdata time
set timefmt "%B %Y"
set format x "%B %Y"
set xtics 24*60*60*30
plot "data" u 6:(1.0) smooth cumulative with lp pt 7
As timefmt
I use only the full month name and the year and ignore the day so that all data points in March are added up, then for April all data points from March and April are summed up etc. With the above data you get the following output image: