Yes, the company you work for can ask you to do this, especially since notice of this policy is given in the company handbook. The fact is that "at will" employers can set the conditions of the workplace much as it sees fit. This includes the right of inspection of a worker's personal property. Accordingly, unless this action violates the terms of a union agreement or employment contract, it is legal unless the policy is applied in a discriminatory manner (i.e. it is only enforced against some workers but not others due to their race, religion, disability, age (over 40), national origin, etc.). For your part, you can comply with the policy, refuse to follow it but risk termination, or quit.