Symbol for circlearrowleft with dot at centre

Question

I am searching for a way to create \circlearrowleft but with dot at its centre (as in \odot) .

I have searched every where, but couldn't find this particular symbol in any LaTeX help/documentation. I will be very thankful for help regarding this.

Answer 1

EDITED to make \dcirclearrowleft of type \mathrel.

\documentclass{article}
\usepackage{amssymb,stackengine}
\newcommand\dcirclearrowleft{\mathrel{%
  \ensurestackMath{\stackengine{0pt}{\circlearrowleft}{\cdot}{O}{c}{F}{T}{L}}%
}}
\begin{document}
$A \dcirclearrowleft B$
\end{document}

If it needs to work across math styles:

\documentclass{article}
\usepackage{amssymb,stackengine,scalerel}
\newcommand\dcirclearrowleft{\mathrel{\ThisStyle{%
  \ensurestackMath{\stackengine{0pt}{\SavedStyle\circlearrowleft}%
                                    {\SavedStyle\cdot}{O}{c}{F}{T}{L}}%
}}}
\begin{document}
$
A \dcirclearrowleft B\scriptstyle
A \dcirclearrowleft B\scriptscriptstyle
A\dcirclearrowleft B
$
\end{document}

Answer 2

Using ooalign:

\documentclass[]{article}
\usepackage{amssymb}

\makeatletter
\newcommand{\circdot}{%
  \mathrel{%
    \vphantom{\circlearrowleft}%
    \mathpalette\circd@t\relax
  }%
}
\newcommand{\circd@t}[1]{{\ooalign{%
            $\m@th#1\circlearrowleft$\cr
            \hidewidth$\m@th#1\cdot$\hidewidth\cr}}}
\makeatother
\begin{document}
    \(x\circdot y = a_{\circdot}\)
\end{document}