CO = Conscientious Objector

The Selective Service web site states: 
A conscientious objector is one who is opposed to serving in the armed forces and/or bearing arms on the grounds of moral or religious principles.

The Law states: 
Nothing contained in this title shall be construed to require any person to he subject to combatant training and service in the armed forces of the United States who, by reason of religious training and belief, is conscientiously opposed to participation in war in any form. . . the term "religious training and belief" does not include essentially political, sociological, or philosophical views, or a merely personal moral code. Any person. . . whose claim is sustained by the local board shall, if he is inducted into the armed forces. . . be assigned to noncombatant service. . . or shall, if he is found to be conscientiously opposed to participation in such noncombatant service. . .perform ... civilian work contributing to the maintenance of the national health, safety, or interest. . .  -- Section 6(j) of the Military Selective Service Act. 

Read the S.S. web site CO Fact Sheet
After registering and passing the tests (physical, mental), you can apply for a CO. Only the local draft board can decide if you get the CO, which you can appeal if denied. You can even check your status online.

Excellent links for CO study: 
Biblical/Christian reasons, how to fill out the form, codes and proceedures for all 4 military branches, FAQs about contradictory questions, links to organizations and the Quakers. 

After you study the above: 
Go register for the draft at The Selective Service web site.