In their list of "key issues" on their web site, they certainly don't promote it among the things they stand for (click).
Interesting, in spite of their claim about their mission: "The ACLU is our nation's guardian of liberty, working daily in courts, legislatures and communities to defend and preserve the individual rights and liberties that the Constitution and laws of the United States guarantee everyone in this country."
A quickie internet search for "gun control" on the aclu.org web site shows quite a lot of "hits": click.
Including for this: Second Amendment @ ACLU.org. Their official take on the 2A/RKBA:
Given the reference to "a well regulated Militia" and "the security of a free State," the ACLU has long taken the position that the Second Amendment protects a collective right rather than an individual right. For seven decades, the Supreme Court's 1939 decision in United States v. Miller was widely understood to have endorsed that view. This position is currently under review and is being updated by the ACLU National Board in light of the U.S. Supreme Court decision in D.C. v. Heller in 2008.
Although ACLU policy cites the Supreme Court's decision in U.S. v. Miller as support for our position on the Second Amendment, our policy was never dependent on Miller. Rather, like all ACLU policies, it reflects the ACLU's own understanding of the Constitution and civil liberties.
Heller takes a different approach than the ACLU has advocated. At the same time, it leaves many unresolved questions, including what firearms are protected by the Second Amendment, what regulations (short of an outright ban) may be upheld, and how that determination will be made.
Those questions will, presumably, be answered over time.
In short, they're not a really strong supporter. To say the least.