Question

Which econometric software do you use to apply the Randomized Control Trial Method?

Answer 1

I see nobody has answered this question, so I'll throw my hit in the ring.  

I don't know what you mean by apply?   If you mean estimate the difference based on the collected data, I'm a  stata dude.  If you mean implementation, that most of that happens in microsoft office.  

But  when you have an RCT evaluation is as simple as taking the difference of two means.  Use excel, stata, R, your smartphone, literally whatever you want.

Answer 2

In the ReplicationWiki that I started you can find information on what software was used for published studies that reported results of randomized controlled trials: https://tinyurl.com/RCT-ReplicationWiki Mostly Stata.