Yes you can, but not the latest, CodeIgniter support was dropped at one point, but nothing is stopping you from using the old version of clockwork !
Clockwork is maintained by itsgoingd, with the relevant projects here (https://github.com/itsgoingd)
Clockwork’s codeigniter support was dropped with Clockwork 2, but you can still use Clockwork V1.x (Statement from itsgoingD himself here https://github.com/itsgoingd/clockwork/issues/333), Version 1 can be downloaded at (https://github.com/itsgoingd/clockwork/tree/v1), 1.6 seems to be the last V1 published.
But there are a few caveats, for example, what browser extensions work with Clockwork V1.6 ?