There are some hieroglyph packages for LaTeX, which define all kinds of symbols, e.g. ancient Egyptians walking around, dung beetles, or African birds. Among these is the package phaistos which defines \HPdove. Strictly speaking it is a dove, but honestly, who can tell the difference from such a pictogram?
Thanks to @cfr for reminding me about ethics regarding animals in captivity. I increased the spacing around the bird a little in the hope to meet the legal standards.
\documentclass{article}
\usepackage{phaistos}
\begin{document}
\renewcommand\arraystretch{2}
\begin{tabular}{|c|c|c|}
\hline
\PHdove & \PHdove & \PHdove \\
\hline
\PHdove & \PHdove & \PHdove \\
\hline
\PHdove & \PHdove & \PHdove \\
\hline
\end{tabular}
\end{document}

The Phaistos font is even available in OpenType and thus usable with Xe/LuaLaTeX. For some reason the dove symbol is mirrored and smaller than in the Type 1 version.
What I find most convincing in this approach is that Unicode actually defines this symbol. Therefore it is as easy as hitting the key on your keyboard!
\documentclass{article}
\usepackage{fontspec}
\newfontfamily\phaistos{Phaistos}
%\def\PHdove{{\phaistos\symbol{"101EF}}}
\def\PHdove{{\phaistos }}
\begin{document}
\begin{tabular}{|c|c|c|}
\hline
\PHdove & \PHdove & \PHdove \\
\hline
\PHdove & \PHdove & \PHdove \\
\hline
\PHdove & \PHdove & \PHdove \\
\hline
\end{tabular}
\end{document}

\includegraphics? There doesn't seem much reason to do this bit in TikZ. (That is, if you don't like the Egyptian dove - my thought was also the hieroglyphs packages.) – cfr Aug 12 '16 at 11:39pic. (But the code does not tend to be very pretty or intelligible!) – cfr Aug 12 '16 at 11:42