Improving Contractor Cybersecurity Act This bill prohibits an executive agency from entering into a contract for information technology unless the contractor maintains a vulnerability disclosure policy (VDP) and program. The contractor must report to the Cybersecurity and Infrastructure Security Agency (CISA) of the Department of Homeland Security, within seven days after the VDP is published, information regarding any valid or credible report of a not previously known public vulnerability on a system that uses commercial software or services that affect, or are likely to affect, other parties in government or industry once a patch or viable mitigation is available; and any other situation where the contractor determines it would be helpful or necessary to involve CISA. CISA must submit vulnerabilities to the MITRE Common Vulnerabilities and Exposures database and the National Institute of Standards and Technology National Vulnerability Database.