This is the issue after anki command:
user@linux:~> anki
Traceback (most recent call last):
  File "/usr/bin/anki", line 5, in <module>
    import aqt
  File "/usr/share/anki/aqt/__init__.py", line 12, in <module> 
    from aqt.qt import * 
  File "/usr/share/anki/aqt/qt.py", line 22, in <module>
    from PyQt4.QtWebKit import QWebPage, QWebView, QWebSettings
ImportError: No module named QtWebKit

Here are the depends on my system (I use Education repo to install anki):

Installed Version
Version:             2.0.47-1.4
Provides:            application()
                     appdata()
                     appdata(anki.appdata.xml)
                     application(anki.desktop)
                     mimehandler(application/x-anki)
                     mimehandler(application/x-apkg)
                     anki = 2.0.47-1.4
Prerequires:         /bin/sh
                     /bin/sh
Requires:           /usr/bin/env
                    python-qt4
                    python-sip
                    python-httplib2
                    python-beautifulsoup
                    python-send2trash
                    rpmlib(CompressedFileNames) <= 3.0.4-1
                    rpmlib(PayloadFilesHavePrefix) <= 4.0-1
                    rpmlib(PayloadIsXz) <= 5.2-1
                    /bin/sh
                    /bin/sh
Suggests:           sox
                    MPlayer
                    lame

These packages and libs are not found in my repos:

python-httplib2
python-send2trash
rpmlib(CompressedFileNames) <= 3.0.4-1
rpmlib(PayloadFilesHavePrefix) <= 4.0-1
rpmlib(PayloadIsXz) <= 5.2-1


libqt4-x11,libQtWebKit4, python2-qt4 are installed on my system.

Also there was upgrade info on Anki website that possibly can explain this issue
https://apps.ankiweb.net/docs/beta.html