Declare your tile into an standalone.cls document:
\documentclass[tikz]{standalone}
\begin{document}
\tikz \node[draw=red, thick, minimum size=2cm] {A};
\end{document}
Which produces and adjusted/cropped figure:

And include this graphic file as an image wherever you need. A tabular can be used to organize them into a grid with or without separation between columns and rows.
\documentclass{beamer}
\begin{document}
\begin{frame}{My title}
{\renewcommand{\arraystretch}{0}
\begin{tabular}{*{5}{@{}c}}
\includegraphics[origin=c,angle=0]{mytile} &
\includegraphics[origin=c,angle=90]{mytile} &
\includegraphics[origin=c,angle=180]{mytile} &
\includegraphics[origin=c,angle=270]{mytile} &
\includegraphics[origin=c,angle=0]{mytile} \\
\includegraphics[origin=c,angle=0]{mytile} &
\includegraphics[origin=c,angle=90]{mytile} &
\includegraphics[origin=c,angle=180]{mytile} &
\includegraphics[origin=c,angle=270]{mytile} &
\includegraphics[origin=c,angle=0]{mytile} \\
\includegraphics[origin=c,angle=0]{mytile} &
\includegraphics[origin=c,angle=90]{mytile} &
\includegraphics[origin=c,angle=180]{mytile} &
\includegraphics[origin=c,angle=270]{mytile} &
\includegraphics[origin=c,angle=0]{mytile} \\
\end{tabular}}
\end{frame}
\end{document}

In case you use TikZ to define your figure it's possible to use other solutions to build an array of rotated images. One of them could be to define the main image as a pic and repeat it inside a matrix with no columns and row separation. Some examples are following. The original figure has been taken from looking for Efficient alternative to my tikzpic code.
\documentclass[tikz, border=2mm]{standalone}
\usetikzlibrary{positioning}
\tikzset{
myfigure/.pic={
\fill[black] (0,0) rectangle ++(-1,-1);
\fill[blue] (-1,0) rectangle ++(-3,-1);
\fill[green] (-4,0)-- ++(-1,0)--++(1,-1)--cycle;
\fill[blue] (0,-1) rectangle ++(-1,-3);
\fill[green] (0,-4)-- ++(-1,0)--++(1,-1)--cycle;
\fill[red] (-4,-1)-- ++(0,-3)--++(3,0)--cycle;
}
}
\begin{document}
\begin{tikzpicture}
\matrix[column sep=0pt, row sep=0pt] (A) {
\pic[rotate around={-90:(-2.5,-2.5)}]{myfigure}; &
\pic[rotate around={180:(-2.5,-2.5)}]{myfigure}; \\
\pic{myfigure}; &
\pic[rotate around={90:(-2.5,-2.5)}]{myfigure}; \\};
\matrix[column sep=0pt, row sep=0pt, right=of A] (B){
\pic[rotate around={90:(-2.5,-2.5)}]{myfigure}; &
\pic{myfigure}; \\
\pic[rotate around={180:(-2.5,-2.5)}]{myfigure}; &
\pic[rotate around={-90:(-2.5,-2.5)}]{myfigure}; \\};
\matrix[column sep=0pt, row sep=0pt, below=of A]{
\pic[rotate around={180:(-2.5,-2.5)}]{myfigure}; &
\pic[rotate around={90:(-2.5,-2.5)}]{myfigure}; \\
\pic[rotate around={270:(-2.5,-2.5)}]{myfigure}; &
\pic[rotate around={0:(-2.5,-2.5)}]{myfigure}; \\};
\begin{scope}[shift={(10.5cm,-10.5cm)}]
\pic at (0,0) {myfigure};
\pic[rotate=90] at (0,-1) {myfigure};
\pic[rotate=180] at (1,-1) {myfigure};
\pic[rotate=270] at (1,0) {myfigure};
\end{scope}
\end{tikzpicture}
\end{document}

tile.texinside anstandaloneclass. This way you have a cropped pdf file with your tile. Then you can use\includegraphicsto input and rotate it like you want. – Ignasi Feb 21 '18 at 18:32