AS long as the bottle doesnt say anything about not having the fish in it then it's fine to use.
There are some bottles that will say "not safe to use with scale-less fish and inverts" those are still fine to use with your betta as well, just dont use them with shrimp, snails, or cories.
Something to consider is why you feel you need the clarifier.. if this is a brand new tank you may just be experiencing a bacterial bloom, which is normal, and clarifier won't do anything to fix it, but it will resolve on it's own in 2-3 weeks.
For what it's worth clarifier really only works in some very specific conditions... one of which would be if you have very fine particulate matter suspended in your water (for example you are using sand as a substrate, and didn't rinse it before adding water to the tank, all the dust in your sand is now in the water), but even that will clear up on it's own with some time... clarifier only speeds up the process in that case by allowing the particles to stick to each other... but they still have to settle out or get filtered out.
Cloudy water is usually a symptom of something. In this case it's a new tank, and because it's a new tank it's not a big concern for now - in other cases it could be the start of an algae bloom, an overdose of flourish excel, or any number of other things - but the first step should always be figuring out what the cause is, rather than just trying to eliminate it.. fixing the problem (or waiting it out if it's particulates or just a new tank) usually clears up the water just fine, you don't have to do or add anything else.
we tried it before, the stuff did nothing for the water clarity, and it may actually have killed off two of our goldfish. we're not 100% certain it was the cause, but two of them dropped dead within three days of us using it when they'd been perfectly healthy before.