Can my employer terminate me because I was arrested for a charge that ended up being scratched by the court at my first hearing one week later?

Unless your employer has independent evidence that you committed the alleged crime (for example, a witness), then there may be a state law that makes it illegal to terminate you based strictly on an arrest record.  The state law, if it exists, may apply only to employers of a certain size, such as 15 employees.  If there is no such law in your state, the EEOC has recently began to accept charges that are based on a disparate impact theory for race discrimination.  This means that because statistics show that a higher percent of blacks are arrested compared to whites, then using an arrest has a disparate impact on black employees thereby creating a  race discrimination case. You should speak to an attorney about this