
It's not \mathscr{I}, which is more italic (slanted)
\documentclass{standalone}
\pdfmapfile{+rsfso.map}
\DeclareSymbolFont{rsfso}{U}{rsfso}{m}{n}
\DeclareSymbolFontAlphabet{\mathscr}{rsfso}
\begin{document}
$\mathscr{I}$
\end{document}
The \pdfmapfile is necessary as of today, since it seems that the map file doesn't correctly register into TeX Live. Works with TeX Live 2010 and 2011/testing.

The package mathrsfs defines \mathscr to use the font rsfs10 (or another size), while my definition requests the font rsfso10 (or at different size). This font has been developed by Michael Sharpe (texdoc rsfso), but his package redefines \mathcal instead of using a different command. So I copied the definition from mathrsfs changing rsfs in the font names into rsfso.
The font is just like RSFS, but less slanted. I don't know why the TeX Live manager doesn't add the map file to pdftex.map; but since the trick with \pdfmapline works, why bother?
Well, we should bother if the engine used is Xe(La)TeX, so a bug report will be filed.
The sensible answer is "find a suitable font" (for example, the STIX script I is pretty close, but is perhaps too slanted). Here's a silly answer.
\documentclass{standalone}
\usepackage{tikz}
\usepackage{calligraphy}
\begin{document}
\begin{tikzpicture}[scale=10]
\calligraphy[copperplate,red,heavy,heavy line width=.2cm,light line width=.1cm]
(0.8,0.51) .. controls +(-.1,-.08) and +(0,-.15) .. (0.5,0.6) .. controls +(0,.15) and +(-.13,-.07) .. (0.85,0.72) +(0,0) .. controls +(-.26,-0.07) and +(.12,.15) .. (0.61,0.3) .. controls +(-.12,-.15) and +(0,-.13) .. (.22,.28);
\end{tikzpicture}
\end{document}
which produces:

Apart from the blob at the end, it's pretty close. I know that it's close because I did it by blowing up the image in the post and drawing on top of it. The line widths probably need tweaking a little, but it's only meant to be a silly answer ...
\mathscr{I} wouldn't be acceptable to you.
– Andrew Stacey
Jun 23 '11 at 13:33
calligraphy package is now on CTAN, as a part of package spath3. May this info help those new readers of this answer, like me.
– muzimuzhi Z
Oct 05 '18 at 20:29
Choose another font if needed.
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[charter]{mathdesign}
\begin{document}
\Huge
$\mathfrak{I}
\mathscr{I}$
\end{document}

mathscrversion for me. But I don't know if it has other maths script fonts... – Seamus Jun 23 '11 at 12:25\mathscr{I}is more slanted then I guess that's not what you want. – Andrew Stacey Jun 23 '11 at 12:38\mathscr{I}as well from detexify. (It's a bit easier to scribble if you have a trackpad instead of a mouse.) – David Hammen Jun 23 '11 at 13:00