Define, as already suggested, the macro with "relative units":
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.pathmorphing,shapes}
\newcounter{sarrow}
\newcommand\xrsquigarrow[1]{\mathrel{%
\begin{tikzpicture}[baseline={($(current bounding box.south)+(0,-0.5ex)$)}]
\node[inner sep=.5ex] (\thesarrow) {$\scriptstyle #1$};
\draw[<-,decorate,
decoration={snake,amplitude=0.135ex,segment length=0.34em,pre=lineto,pre length=0.4em}]
(\thesarrow.south east) -- (\thesarrow.south west);
\end{tikzpicture}
}}
\begin{document}
$A\xrsquigarrow{f}B$
{\large$A\xrsquigarrow{f}B$\par}
{\Large$A\xrsquigarrow{f}B$\par}
{\LARGE$A\xrsquigarrow{f}B$\par}
{\small$A\xrsquigarrow{f}B$\par}
{\footnotesize$A\xrsquigarrow{f}B$\par}
\end{document}
In order to get automatic scaling for subscripts and superscripts (or \scriptstyle declarations), one has to work harder:
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.pathmorphing,shapes}
\makeatletter
\newcommand\xrsquigarrow[1]{\mathrel{\mathchoice
{\hbox{\fontsize{\tf@size}{\tf@size}\selectfont\@xrsquigarrow\scriptstyle{#1}}}
{\hbox{\fontsize{\tf@size}{\tf@size}\selectfont\@xrsquigarrow\scriptstyle{#1}}}
{\hbox{\fontsize{\sf@size}{\sf@size}\selectfont\@xrsquigarrow\scriptscriptstyle{#1}}}
{\hbox{\fontsize{\ssf@size}{\ssf@size}\selectfont\@xrsquigarrow\scriptscriptstyle{#1}}}
}}
\newcommand\@xrsquigarrow[2]{%
\begin{tikzpicture}[baseline={($(current bounding box.south)+(0,-0.5ex)$)}]
\node[inner sep=.5ex] (A) {$#1#2$};
\draw[<-,decorate,
decoration={snake,amplitude=0.135ex,segment length=0.34em,pre=lineto,pre length=0.4em}]
(A.south east) -- (A.south west);
\end{tikzpicture}%
}
\begin{document}
$A\xrsquigarrow{f}B_{A\xrsquigarrow{f}B}$
{\large$A\xrsquigarrow{f}B$\par}
{\Large$A\xrsquigarrow{f}B$\par}
{\LARGE$A\xrsquigarrow{f}B$\par}
{\small$A\xrsquigarrow{f}B$\par}
{\footnotesize$A\xrsquigarrow{f}B$\par}
\end{document}
Beware that this is slow, because for each instance of \xrsquigarrow all the four variants need to be typeset.
Note. I've removed \thesarrow that does nothing more than provide a node name.
\mathchoice requires four arguments: what's to be typeset in display, text, first level sub/superscript and second level sub/superscript styles respectively. All four text will be typeset and then TeX will decide which one to use. So we set four boxes in which the font is chosen to be of size \tf@size for display and text styles, \sf@size and \ssf@size for the other two styles (these sizes are automatically computed by LaTeX when a formula is being typeset).
The box then contains \@xrsquigarrow which has two arguments: the style to be applied for the label and the label itself. This style should be \scriptstyle when the arrow is in display or text styles, \scriptscriptstyle in the other cases.
The definition of \@xrsquigarrow, apart from the additional parameter, is just the same as the one proposed before.
Best Answer
State
#2\smaller.