Can a person chrged with a crime and not yet convicted be denied employment?

What kind of job? What country? WHat state?

You say "not yet convicted" does that mean they are still pending trial, that they are charged, and will have to go to court still ?

Short answer, yes. You have no right to employment and an employer can fail to hire you for no reason at all. However. We could benefit from knowing the details of the charges and the type of job.

Received a speeding ticket,and DUI0.09.

Applied for job as custodian.

Unless you are being discriminated against - yes, they hired other people facing the same charges - you have no case.

It's employment at will. They can hire (or fire) anyone they want to hire/fire unless there's a union or employment contract.

I guess first how did they know about it, since arrests don't show up on police back ground checks, and often not even private checks for a bit.

So unless you tell them how will they know.

But if the job requires you to drive one of their autos, that can be an issue

Many employers will pass on someone who has a drinking problem and even smokers. Drives up their health plan costs.

Yes, they can legally not hire you if they so choose to. This would not be discrimination as it has nothing to do with race, religion, and being handicapped which are the only reasons you would be able to fight this. Having a DUI is not being discriminated against.