8 USC 1187(a)(5) establishes the "signatory carrier" requirement, but the requirement is somewhat broader than that:
(5) Entry into the United States
If arriving by sea or air, the alien arrives at the port of entry into the United States on a carrier, including any carrier conducting operations under part 135 of title 14, Code of Federal Regulations, or a noncommercial aircraft that is owned or operated by a domestic corporation conducting operations under part 91 of title 14, Code of Federal Regulations which has entered into an agreement with the Secretary of Homeland Security pursuant to subsection (e). The Secretary of Homeland Security is authorized to require a carrier conducting operations under part 135 of title 14, Code of Federal Regulations, or a domestic corporation conducting operations under part 91 of that title, to give suitable and proper bond, in such reasonable amount and containing such conditions as the Secretary of Homeland Security may deem sufficient to ensure compliance with the indemnification requirements of this section, as a term of such an agreement.
Subsection (e) concerns the agreement -- the thing the signing of which earns the carrier the designation "signatory":
(e) Carrier agreements
(1) In general
The agreement referred to in subsection (a)(4) is an agreement between a carrier (including any carrier conducting operations under part 135 of title 14, Code of Federal Regulations) or a domestic corporation conducting operations under part 91 of that title and the Secretary of Homeland Security under which the carrier (including any carrier conducting operations under part 135 of title 14, Code of Federal Regulations) or a domestic corporation conducting operations under part 91 of that title agrees, in consideration of the waiver of the visa requirement with respect to a nonimmigrant visitor under the program—
(A) to indemnify the United States against any costs for the transportation of the alien from the United States if the visitor is refused admission to the United States or remains in the United States unlawfully after the 90-day period described in subsection (a)(1)(A),
(B) to submit daily to immigration officers any immigration forms received with respect to nonimmigrant visitors provided a waiver under the program,
(C) to be subject to the imposition of fines resulting from the transporting into the United States of a national of a designated country without a passport pursuant to regulations promulgated by the Secretary of Homeland Security, and
(D) to collect, provide, and share passenger data as required under subsection (h)(1)(B).
(2) Termination of agreements
The Secretary of Homeland Security may terminate an agreement under paragraph (1) with five days’ notice to the carrier (including any carrier conducting operations under part 135 of title 14, Code of Federal Regulations) or a domestic corporation conducting operations under part 91 of that title for the failure by a carrier (including any carrier conducting operations under part 135 of title 14, Code of Federal Regulations) or a domestic corporation conducting operations under part 91 of that title to meet the terms of such agreement.
(3) Business aircraft requirements
(A) In general
For purposes of this section, a domestic corporation conducting operations under part 91 of title 14, Code of Federal Regulations 1 that owns or operates a noncommercial aircraft is a corporation that is organized under the laws of any of the States of the United States or the District of Columbia and is accredited by or a member of a national organization that sets business aviation standards. The Secretary of Homeland Security shall prescribe by regulation the provision of such information as the Secretary of Homeland Security deems necessary to identify the domestic corporation, its officers, employees, shareholders, its place of business, and its business activities.
(B) Collections
In addition to any other fee authorized by law, the Secretary of Homeland Security is authorized to charge and collect, on a periodic basis, an amount from each domestic corporation conducting operations under part 91 of title 14, Code of Federal Regulations, for nonimmigrant visa waiver admissions on noncommercial aircraft owned or operated by such domestic corporation equal to the total amount of fees assessed for issuance of nonimmigrant visa waiver arrival/departure forms at land border ports of entry. All fees collected under this paragraph shall be deposited into the Immigration User Fee Account established under section 1356(h) of this title.