Claims to copyright in published or unpublished musical works can be registered in the Copyright Office.

Published collections of musical works and all the copyrightable elements of a unit of publication can be submitted for registration on one application with a single fee if all the compositions are owned by the same copyright claimant. For details on deposit requirements for published musical works, see Circular 50, Copyright Registration for Musical Compositions.

Unpublished collections of two or more musical works can be submitted for registration on one application with a single fee and a deposit of one complete copy or phonorecord if all the conditions specified in Circular 50 under the heading “Collections of Music” are met.

Follow this link for more information and to Register your song(s) Online:
Copright.gov

Mailing Address for Applications Filed on
Paper and for Hard-copy deposits

Library of Congress
U.S. Copyright Office–PA
101 Independence Avenue, SE
Washington, DC 20559

Online registration
-the preferred way to register basic
claims for literary works; visual arts works; performing arts
works, including motion pictures; sound recordings; and
single serials. Advantages of online filing include:
•a lower filing fee
•fastest processing time
•online status tracking
•secure payment by credit or debit card, electronic check,
or Copyright Office deposit account
•the ability to upload certain categories of deposits directly
as electronic files

Detailed Information Here:
Circular 50 Copyright PDF