Silent Installation of RStudio

While installing the application RStudio silently the application only install it through Administrative Account. Is there any way to install it via other user who has No Administrator level permission?

Following what you've said it seems you're trying to install RStudio on a computer which hast restricted access levels for users.
In case your network Admin restricted your user not to install any programs you should ask him to install it for you maybe. Or maybe he avoids only to install it in specific folders - depends on his policy.
An option could be to try to install RStudio in your personal folder where you should have write access.

RStudio provides installer-less bundles -- see the Zip / Tarballs section; e.g. at:

In general, you can unpack those tarballs wherever you'd like, and then run bin/rstudio within the unpacked archive to run RStudio.