Creating a new symbol in LaTeX

I provide, at no cost to you, froogle...works in all math styles.

documentclass{article}
usepackage{graphicx,scalerel}
newcommandfroogle{scalerel*{rotatebox{90}{raisebox{1pt}{%
  scalebox{1}[.7]{$varsigma$}}kern-1.1ptscalebox{.7}[1]{o}}}{Xg}}
begin{document}
$froogle(x) + A_{froogle_{(1 + froogle)}}$
end{document}

If you change fonts, the parameters may need tweaking. Here, I redo for txfonts:

documentclass{article}
usepackage{graphicx,scalerel,txfonts}
newcommandfroogle{scalerel*{rotatebox{90}{raisebox{1.3pt}{%
  scalebox{.85}[.7]{$varsigma$}}kern-1.2ptscalebox{.85}[1]{o}}}{Xg}}
begin{document}
$froogle(x) + A_{froogle_{(1 + froogle)}}$
end{document}

I think that you can find three symbols that are close to one you desire. The $varrho$ from Fran's answer, and two mathfrak characters (the g and d, transformed).

The code is here.

documentclass[11pt, border=1cm]{standalone}
usepackage{amssymb}
usepackage{graphicx}

begin{document}

$xmapstovarrho(x)$ 
qquad
$xmapstoraisebox{-.2ex}{rotatebox[origin=c]{180}{$mathfrak{d}$}}(x)$
qquad
$xmapstoraisebox{.35ex}{reflectbox{$mathfrak{g}$}}(x)$
end{document}