How can I rotate \in by 90 degrees?

The result is really ugly:

\documentclass{article}
\usepackage{graphicx,amssymb}
\newcommand{\vin}{\rotatebox[origin=c]{-90}{$\in$}}
\begin{document}
\[
\begin{array}{@{}c@{\;}c@{\;}c@{\;}c@{\;}c@{}}
x & \cdot & W_{1,2} & = & o \\
\vin && \vin && \vin \\
\mathbb{R}^{1\times n} && \mathbb{R}^{n\times m} && \mathbb{R}^{1\times m}
\end{array}
\]
\end{document}

I'd simply avoid such visual description in print; I often use something like that on the blackboard, but it's a completely different situation. I'd prefer something like

\[
x\cdot W_{1,2} = o
\]
where $x\in\mathbb{R}^{1\times n}$ and $W_{1,2}\in\mathbb{R}^{n\times m}$.

in a printed document.

You could try the \usepackage{rotating} package and use the \begin{rotate}{30}...\end{rotate} environment.

Or use the approach described in Rotated $\ltimes$ symbol (\rotatebox command from the graphicx package).