Beginning in RStudio 0.99, RStudio Desktop is not compatible with RHEL 6/CentOS 6. This isn't due to a requirement in RStudio itself but rather a dependency on glibc 2.14 in Qt 5.4, which is the framework on which many elements of RStudio's cross-platform user interface are built.
If you need to run RStudio on a RHEL/CentOS 6 machine, you might consider installing RStudio Server instead. RStudio Server does not use Qt and thus doesn't have the glibc requirement. Like RStudio Desktop, RStudio Server can be run entirely offline on a single desktop computer.
Another way around the problem is to use a version of RStudio Desktop built on an older version of Qt. The last version available is 0.98.1103, which you can find on our Older Versions of RStudio download page.
Finally, if you're technically inclined, there are ways to produce Qt builds on older glibc if you're willing to build Qt yourself. There are also some mechanisms for running multiple glibc versions side-by-side (usually in a primary/secondary configuration). We can't provide specific help with these since they're very dependent on your local environment.
We're hoping to remove the glibc 2.14 requirement in an upcoming version of RStudio.