You can use the picture environment:
\documentclass{article}
\usepackage{pict2e,picture}
\newcommand{\triplus}{\mathbin{
\sbox0{$+$}
\begin{picture}(\wd0,\ht0)
\put(0,0){\line(1,.577){.5\wd0}}
\put(.5\wd0,.289\wd0){\line(-1,.577){-.5\wd0}}
\put(.5\wd0,.289\wd0){\line(0,1){\dimexpr\ht0-.289\wd0\relax}}
\end{picture}
}
}
\begin{document}
$a+b\triplus c$
\end{document}

Adding \roundcap, as suggested by Heiko Oberdiek, might be even better:
\documentclass{article}
\usepackage{pict2e,picture}
\newcommand{\triplus}{\mathbin{
\sbox0{$+$}
\begin{picture}(\wd0,\ht0)
\roundcap
\put(0,0){\line(1,.577){.5\wd0}}
\put(.5\wd0,.289\wd0){\line(-1,.577){-.5\wd0}}
\put(.5\wd0,.289\wd0){\line(0,1){\dimexpr\ht0-.289\wd0\relax}}
\end{picture}
}
}
\begin{document}
$a+b\triplus c$
\end{document}
