Do RQM support the security standard ISO 27001?

RQM is not ISO 27001 certified.  CLM 4.0.4 does provide support for the National Institute of Standards and Technology (NIST) standard SP 800-131A (see https://jazz.net/downloads/rational-quality-manager/releases/4.0.4?p=news#TOC_C).

I don't think asking whether CLM is ISO 27001 certified makes as much sense as asking whether CLM can either expose you in ISO 27001 certification and/or help you realize certification within your company.

For instance:
Paul Slauenwhite's mention of NIST SP 800-131A adoption enables you to meet "Network security".
The customizable Lab Management capability within QM can be used to facilitate "Asset Management".
CLM integrates with best-of-breed LDAP configurations for "User Registration" and "Password Management".

Hope this helps.
John Nason
QM Development