Can I be fired from my job for refusing to sign a non-compete agreement?

Yes, you can be fired for this. An "at will"employer has a great deal of discretion in setting the terms and conditions of employment. Absent an employment contract or union agreement to the contrary, or if this this mandate violates existing company policy, or some form of actionable discrimination is present, you must sign this agreement or lose your job.  That is assuming the non-compete is enforceable under your state law.

The fact is that best time to have an employee sign a non-compete agreement is the period before they start employment, since the courts have held that the commencing the employment relationship provides sufficient consideration to support the restrictive covenant. In PA, in order to enter into a non-compete agreement once an employee is already working for an employer, there must be some new consideration. In other words, the employer must provide the employee with some sufficiently beneficial change in status. For example, offering a sufficient decree of benefits -  a bonus, a promotion, a raise, and/or an increase in benefits.

Additionally, a non-compete agreement must be reasonable as to both time and geographic scope. Courts ask whether restricting the employee to the designated time and area is reasonably necessary to protect the legitimate business interests of the employer. If the restriction is deemed overly broad, it will fail.

If an employee is is discharged based on the failure to sign an unenforceable non-compete, they can sue for wrongful termination. At this point, you will need to consult directly with an employment law attorney in your area who can review your agreement and determine is legality.