\documentclass{article}
\usepackage{amssymb,pict2e}
\newcommand{\danucircle}{\mathord{\mathpalette\dodanucircle\relax}}
\newcommand{\dodanucircle}[2]{%
\sbox0{$#1\square$}%
\setlength{\unitlength}{\ht0}%
\begin{picture}(1.2,1)
\put(0.6,0.5){\circle{1}}
\end{picture}%
}
\begin{document}
$\triangle\square\danucircle\square$
\end{document}