Spyder plugin support will be released with version 3.0 (Still in Beta).
If you want to try out this plugin you need to use the latest development version of Spyder (master branch).
See https://github.com/spyder-ide/spyder/wiki/User-plugins, but in short:
pip install spyder.autopep8
Press Shift+F8 (default) to run autopep8 on the current file or go to
Source > Run autopep8 code autoformatting.
If some text is selected, autopep8 will run on this text only.
Informations about the execution will be displayed in the statusbar.