Which RPA tool should I learn being a C# Developer
Blue Prism is a good tool to start learning RPA with, but as Andrzej already pointed out: it's not free. Not even a little bit!
UIPath, however, is free! (for small enterprises). The coding is in VB, which is .NET's predecessor. UIPath is also growing and used (currently) mostly in Eastern Europe (as far as I know).
In my opinion though: you're a developer. Whatever RPA tool you'll pick up is going to be child's play as there's very little coding involved among the more popular RPA tools.
Now that Automation Anywhere launched their own free community version, I will alter my previous statement:
"Either UiPath or Automation Anywhere are good starting points for new RPA Developers. I've worked with both for quite some time and they both have their pros and cons. A lot comes down to personal preference. In the end; if you know one, you will more easily pick up another."
As @Sergiu pointed out, this thread has become somewhat dated and so has this answer. The answer itself remains valid though, as UiPath still employs VB (.NET) most extensively in comparison to the other popular RPA tools.
That being said, UiPath has (according to Gartner) become the most used RPA tool worldwide, which arguably makes this answer all the more viable. Note though, that nowadays, BluePrism and Automation Anywhere also have community editions.
This would make BluePrism a notable contender for the OP's answer, but market-wise, I still suggest going for (sticking to?) UiPath.
I will suggest as a .NET developer go for UI Path its community version is free and also available with trial version. It uses internally .NET syntax in it's activities and control.
Automation Anywhere claims to be for non-programmers. You will be very frustrated with the poor syntax and limitations. If you are a good C# programmer go for Open Source Selenium that will allow you to easily automate web applications. Most of what you probably want from an RPA product.