It is easy enough to implement using \pgfpatharcaxes and \pgfpointpolarxy.
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[red] (0,0) arc[x radius=2, y radius=1, rotate=-45,
start angle=0, end angle=180];
\pgfpathmoveto{\pgfpointorigin}
\pgfpatharcaxes{0}{180}{\pgfpointpolarxy{-45}{2}}%
{\pgfpointpolarxy{-45+90}{1}}
\pgfusepath{draw}
\end{tikzpicture}
\end{document}


\drawas an option – percusse Jan 17 '18 at 16:34[rotate=-45]just beforearc[...]:\draw[red] (0,0) [rotate=-45] arc[x radius=2, y radius=1, start angle=0, end angle=180];. – Paul Gaborit Jan 17 '18 at 16:48