The question linked above is related, but it is about fitting with the text width. Hence I hope the following will be useful.
With tikzscale:
\documentclass{beamer}
\usepackage{tikz}
\usepackage{tikzscale}
\usepackage{filecontents}
\begin{filecontents*}{myfig.tikz}
\begin{tikzpicture} %
\draw[color=blue, fill=blue] (0,0) .. controls (5.30, 1.76) and (10.55, 1.32) .. (10.61, 1.32) -- (10.61, 1.75) -- (0,1.75) -- (0,0);
\end{tikzpicture}
\end{filecontents*}
\begin{document}
\begin{frame}{A Frame}
\begin{center}
\makebox[0pt]{%
\includegraphics[width=\paperwidth]{myfig.tikz}
}
\end{center}
\end{frame}
\end{document}
With adjustbox:
\documentclass{beamer}
\usepackage{tikz}
\usepackage{adjustbox}
\begin{document}
\begin{frame}{A Frame}
\begin{adjustbox}{width=\paperwidth,center}
\begin{tikzpicture} %
\draw[color=blue, fill=blue] (0,0) .. controls (5.30, 1.76) and (10.55, 1.32) .. (10.61, 1.32) -- (10.61, 1.75) -- (0,1.75) -- (0,0);
\end{tikzpicture}
\end{adjustbox}
\end{frame}
\end{document}
On barefoot:
\documentclass{beamer}
\usepackage{tikz}
\begin{document}
\begin{frame}{A Frame}
\begin{center}
\makebox[0pt]{\resizebox{\paperwidth}{!}{%
\begin{tikzpicture} %
\draw[color=blue, fill=blue] (0,0) .. controls (5.30, 1.76) and (10.55, 1.32) .. (10.61, 1.32) -- (10.61, 1.75) -- (0,1.75) -- (0,0);
\end{tikzpicture}%
}%
}
\end{center}
\end{frame}
\end{document}

tikzscale, see [tag:tikzscale]. – Qrrbrbirlbel Sep 02 '13 at 13:32