\newcommand{\Rsqr}[1][]{\ensuremath{\mathrm{R_{#1}^2}}}
1. The \ensuremath command essentially ‘makes it work’ in both math and text mode.
2. I allowed the parameter to have a default (in this case a ‘blank’ default) as specified by the empty square brackets. But here’s the important part: when actually specifying the parameter (i.e. not using the default), it is necessary to now use square brackets instead of the usual {} that I have become used to with \newcommand. For example: \Rsqr[adj] works but \Rsqr{adj} does not!