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}
