A better notation to denote arcs for an American high school textbook

tipa's \texttoptiebar looks useable:

\documentclass{article}
\usepackage{graphicx,tipa}% http://ctan.org/pkg/{graphicx,tipa}
\newcommand{\arc}[1]{{%
  \setbox9=\hbox{#1}%
  \ooalign{\resizebox{\wd9}{\height}{\texttoptiebar{\phantom{A}}}\cr#1}}}
\begin{document}
\arc{AC}\ \arc{BAD}\ \arc{ICK}\ \arc{GOOD}
\end{document}

A solution along the lines of Werner's, but that avoids its shortcomings, first of all the dependency on tipa:

\documentclass{article}
\usepackage{graphicx}

\makeatletter
\DeclareFontFamily{U}{tipa}{}
\DeclareFontShape{U}{tipa}{m}{n}{<->tipa10}{}
\newcommand{\arc@char}{{\usefont{U}{tipa}{m}{n}\symbol{62}}}%

\newcommand{\arc}[1]{\mathpalette\arc@arc{#1}}

\newcommand{\arc@arc}[2]{%
  \sbox0{$\m@th#1#2$}%
  \vbox{
    \hbox{\resizebox{\wd0}{\height}{\arc@char}}
    \nointerlineskip
    \box0
  }%
}
\makeatother

\begin{document}

$\arc{AC}$ $\arc{BAD}$ $\arc{ICK}$ $\arc{GOOD}_{\arc{xyz}}$

\end{document}

A different solution with the yhmath font:

\documentclass{article}

\DeclareFontFamily{OMX}{yhex}{}
\DeclareFontShape{OMX}{yhex}{m}{n}{<->yhcmex10}{}
\DeclareSymbolFont{yhlargesymbols}{OMX}{yhex}{m}{n}
\DeclareMathAccent{\wideparen}{\mathord}{yhlargesymbols}{"F3}

\begin{document}

$\wideparen{AC}$ $\wideparen{BAD}$ $\wideparen{ICK}$ $\wideparen{GOOD}_{\wideparen{xyz}}$

\end{document}