It takes around one month to learn the basics of R, assuming you spend an hour a day devoted to your studies.
If you want to use R in a professional environment, you can expect to spend at least six months developing the knowledge you need.
R is very different from many programming languages. Like any programming language, it's hard to estimate how long it will take you to learn it.
While a technical background will help you, even beginner concepts will be unfamiliar to many programmers.
What's more, thousands of packages out there extend upon R. These packages are written to apply R in various specific contexts.
You can expect to spend months learning to use some more extensive packages.