Is there a way to get the Skype logo in the cvtheme document class?

It's included in the latest version of font awesome. There is a LaTeX package for Font Awesome, but it doesn't include a command for the Skype logo, so you have to add it manually.

\documentclass{article}
\usepackage{fontawesome}
\newcommand\faSkype{{\FA\symbol{"F17E}}}
\begin{document}
    \noindent
    \faSkype{} Skype \\
    \faPhone{} Phone \\
    \faFacebookSign{} Facebook
\end{document}

Another solution I can think of is manually accessing it. Here's how:

\documentclass{article}
\usepackage{fontspec}
\newfontfamily\fontawesome
    [ Path = /Path/to/font-awesome-4.0.1/fonts/ ,
      Extension = .otf ]
    {FontAwesome}
\newcommand\fasymbol[1]{{\fontawesome\symbol{"F#1}}}
\newcommand\faSkype{\fasymbol{17E}}
\newcommand\faPhone{\fasymbol{095}}
\newcommand\faFacebook{\fasymbol{082}}
\begin{document}
\noindent
\faSkype{} Skype \\
\faPhone{} Phone \\
\faFacebook{} Facebook
\end{document}

For the symbol codes you can check the cheatsheet on their site. You'll find the icon name (eg: fa-skype) along with the hexadecimal unicode code for the symbol (eg: ). From the unicode code you can use the last three numbers/letters in capitals (17E) in the custom \fasymbol command. For this example I've created three macro's.