`\stackrel` but lower

Not \ooalign, which superimposes symbols: you need to stack them, so \ialign is better.

\documentclass{article}
\usepackage{amsmath,mathtools}

\makeatletter
\DeclareRobustCommand{\frtimes}{\mathbin{\mathpalette\frtimes@@\relax}}
\newcommand{\frtimes@@}[2]{%
  \vbox{\offinterlineskip
    \sbox\z@{$\m@th#1\times$}%
    \ialign{%
      \hfil##\hfil\cr
      $\m@th#1{}_{\frown}\kern-\scriptspace$\cr
      \noalign{\kern-.3\ht\z@}
      \box\z@\cr
    }%
  }%
}
\makeatother

\begin{document}

$A\frtimes B_{A\frtimes B}$

\end{document}

Here are three other solutions: one with stackengine, and the other ones replacing \frown with the\wideparen math accent, from mathabx and yhmath respectively.

\documentclass[border=5pt]{standalone}
\usepackage[usestackEOL]{stackengine} %
\usepackage{accents}
\newcommand\frimes{\mathbin{\ensurestackMath{\stackon[-1pt]{\times}{\frown}}}}

\DeclareFontFamily{U}{mathx}{\hyphenchar\font45}
\DeclareFontShape{U}{mathx}{m}{n}{
<5><6><7><8><9><10>
<10.95><12><14.4><17.28><20.74><24.88>
mathx10
}{}
\DeclareSymbolFont{mathx}{U}{mathx}{m}{n}
\DeclareFontSubstitution{U}{mathx}{m}{n}
\DeclareMathAccent{\varwideparen}{0}{mathx}{"8C}

\DeclareSymbolFont{largesymbols}{OMX}{yhex}{m}{n}
\DeclareMathAccent{\wideparen}{\mathord}{largesymbols}{"F3}

\begin{document}

$
a
\frimes
b
\quad
a
\mathbin{\varwideparen{\times}}
b
\quad
a
\mathbin{\wideparen{\times}}
b$

\end{document} 

I think an easy way is to create an array, as suggested by Werner

\documentclass[border=5pt]{standalone}
\begin{document}
$
a
\begin{array}[b]{@{}c@{}}
  \frown       \\ [-7pt] % adjust as needed
  {} \times {} \\
\end{array}
b
$
\end{document}

yielding