Direct proof of use
Anti-ship cruise missile use in the 1990 Gulf War is directly documented in the February 25, 1991 naval engagement off Kuwait. A U.S. Department of Defense GulfLINK chronology records HMS Gloucester escorting USS Missouri in the Arabian Gulf when it destroyed an incoming Iraqi Silkworm missile aimed at Missouri with two Sea Dart missiles; the same entry says a second Silkworm was fired but fell into the Gulf and U.S. Navy aircraft destroyed the launch site.
The Battleship Missouri Memorial describes the same event during Missouri's amphibious-feint operation near Kuwait, stating that a Silkworm appeared to be headed toward the battleship and HMS Gloucester fired two Sea Dart missiles to intercept it. The Strauss Center's anti-ship cruise missile overview also lists Operation Desert Storm as a historical ASCM use case, noting an Iraqi Silkworm launch in the Gulf that was intercepted by HMS Gloucester.
Sources: United States Navy in Desert Shield/Desert Storm, Battleship Missouri Gulf War History, Strait of Hormuz Missiles
Timeline
On February 24, 1991, the coalition ground offensive began while U.S., British, Saudi, and Kuwaiti naval forces conducted carrier air, mine-clearance, amphibious, and fire-support missions along Kuwait's coast. GulfLINK records USS Missouri and USS Wisconsin firing at targets in occupied Kuwait in support of that offensive.
On February 25, Missouri continued naval gunfire and amphibious-deception operations near Kuwait. During that activity, Iraqi forces fired Silkworm missiles from shore; HMS Gloucester destroyed the missile assessed as inbound toward Missouri, another Silkworm fell into the Gulf, and follow-on U.S. naval aviation destroyed the launch site.
Sources: United States Navy in Desert Shield/Desert Storm, Battleship Missouri Gulf War History
Operational role
In this conflict record, the documented user was Iraq and the role was coastal anti-ship strike against coalition naval forces operating in the northern Gulf. The public sources identify the missile type as Silkworm, a Chinese-derived anti-ship cruise missile family, and place its use in a shore-launch context against a U.S. battleship task group supporting the ground campaign.
The documented effect was defensive reaction rather than ship damage: Missouri used countermeasures, Gloucester intercepted the inbound missile with Sea Dart, the second missile fell into the water, and the launch site was later attacked. Public sources used here do not support attributing a successful Iraqi anti-ship missile hit, coalition casualties, or ship loss to the February 25 launches.
Sources: United States Navy in Desert Shield/Desert Storm, USS Missouri under Attack by Iraqi Silkworm, Battleship Missouri Gulf War History, Strait of Hormuz Missiles