How to avoid the "http:" part in hyperref's \url?

It's better to use a different command, so that its usage is clear:

\documentclass{article}
\usepackage{xcolor}
\usepackage[
  colorlinks,
  linkcolor=magenta
]{hyperref}
\newcommand\rurl[1]{%
  \href{http://#1}{\nolinkurl{#1}}%
}

\begin{document}
This is a link \rurl{ipython.org} written in abbreviated form.
\end{document}

Of course you lose the tricks \url and \href are able to do with complex URI, for handling special characters, but short URI like this one should not have this problem.

The color in the image shows that it's indeed a link to a Web page.

You can load the package url and redefine the command \url as follows:

\DeclareUrlCommand\url{\color{magenta}\def\UrlLeft{http://}\urlstyle{tt}}

Note that the xcolor package is required, too, if you want to give a color to the link.

Now you can simply write

\url{ipython.org}

and http:// is added automatically.

Complete example

\documentclass{article}
\usepackage{hyperref}

\usepackage{xcolor,url}

\DeclareUrlCommand\url{\color{magenta}\def\UrlLeft{http://}\urlstyle{tt}}

\begin{document}

\url{ipython.org}

\end{document} 

Output:

---

Of course, you can leave the \url command as is and define a new command \shorturl so to have

\documentclass{article}
\usepackage[colorlinks]{hyperref}

\usepackage{xcolor,url}

\DeclareUrlCommand\shorturl{\color{magenta}\def\UrlLeft{http://}\urlstyle{tt}}

\begin{document}

\url{local-link}

\shorturl{ipython.org}

\end{document} 

Output: