There is a possibility: Codeweaver's Crossover Office. This is a specially patched version of winex (a software that let's you run windows binaries on a Linux system). You have to buy the Codeweaver version or you try normal wine which is available for free but probably doesn't work that well with IE.
However, don't even bother. Running binaries on their non-native platform through any sort of emulator never comes close to the performance you get when you run them on the native platform.
Check out the dozens of browsers that are available for linux natively. Mozilla, Galeon, Konqueror, Epiphany, Netscape, lynx ,.... you'll find something you like and that works for you.
If you want to use windows software, use windows.