You should be able to do this by using the python in your virtual environment:
/home/my/virtual/bin/python /home/my/project/manage.py command arg
EDIT: If your django project isn’t in the PYTHONPATH, then you’ll need to switch to the right directory:
cd /home/my/project && /home/my/virtual/bin/python ...
You can also try to log the failure from cron:
cd /home/my/project && /home/my/virtual/bin/python /home/my/project/manage.py > /tmp/cronlog.txt 2>&1
Another thing to try is to make the same change in your manage.py script at the very top:
#!/home/my/virtual/bin/python