In 2005 I was arrested for misdemeanor possession of marijuana and was convicted and was fined $200. But I neglected to pay the fine and now I believe I have a warrant for failure to appear/pay. Will this cause me to lose my employment due to a background check?

It can yes, depending on the company you work for. If you go and take care of the warrant it will disappear from the record.

But I live in Cali and warrant is out of Rhode Island! Any way of taking care of it here in Cali!

Any way of taking care of it if out of state?

Hire an attorney in RI, have them review this and see if you can just pay the fine and penalties and deal with it that way.

If not, see if he can arrange you to fly in, appear in court without arrest, and then pay the fine and be done with it.

Ok, at the worst a plane ticket but what is worst, losing and not getting a job ?