I'm not sure if this will work, but I had a quick look in ICQ preferences and in the Security tab there's a check box that has "Allow others to view my online / offline presence from the web." You could try unchecking that box, although it probably wont fix your problem.
If the spam comes in the form of URLs, you can set your ICQ to decline all incoming addresses in the Events section of Preferences.
It probably wont fix your problem as I have the feeling you're getting text messages, but I guess it's worth a try. Have you looked at the ICQ help pages?
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