"Compliance with ESIGN" is only necessary when you want to deliver electronic documents and count them as the legal equivalent of paper documents. Primarily, the need to assure equivalence arises when documents contain disclosures that a federal law or regulation (Regulations B or Z, for example) require you to deliver "in writing."
To determine whether or not ESIGN is applicable in your case, make a list of all forms, notices, disclosures, and other documents you are required to present to each credit card applicant in writing. If you used to deliver them on paper and now want to use some type of electronic alternative, you must obtain each applicant's consent in the ESIGN-prescribed manner.
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...gone fishing.