A (in my eyes) simple way to do this is the following:
\documentclass{scrartcl}
\usepackage{lipsum}
\usepackage{rotating}
\usepackage{calc}
\begin{document}
\lipsum
\clearpage
\rotatebox{90}{
\begin{minipage}[c]{\textheight-\footskip}
\lipsum[1-2]
\end{minipage}
}
\clearpage
\lipsum
\end{document}
In this MWE I used a \rotatebox{90} do turn a minipage around by 90°. This minipage has the \textheight as its width, so it fits after turned. I subtracted the \footskip, so the minipage doesn't get in the page number's way.
Edit: Since I seem to have misunderstood the question, here is an approach that actually turns the page around by 90° (based on this German tutorial):
\documentclass[paper=a4]{scrartcl}
\usepackage{lipsum}
\usepackage{calc}
\newlength{\oldwidth}
\setlength{\oldwidth}{\textwidth}
\newlength{\oldheight}
\setlength{\oldheight}{\textheight}
\begin{document}
\lipsum
\KOMAoptions{paper=a4,paper=landscape}
\recalctypearea
\areaset{\oldheight+\footskip}{\oldwidth-\footskip}
\lipsum[1-2]
\KOMAoptions{paper=a4,paper=portrait}
\recalctypearea
\areaset{\oldwidth}{\oldheight}
\lipsum
\end{document}
This leads to:
