No, the rules don’t let you do that.
Steal Spell Effect only allows you to steal the effect of a spell, not just any magic. You could make an argument for stealing the effects of spells cast by items (i.e. a wand or scroll), but even that’s not clear. Effects that are just part of wearing the item definitely are not available.
But it would be a cool thing and your DM may allow it
The only reason you can’t is because the rules say “spell.” But they’d still work just as well for magic items: they have Caster Levels to compare against your class level plus Charisma, items can be affected by dispel magic, and so on. Arguably, magic items that apply an effect on whoever wears it has a range of Personal, which is barred, but plenty of items allow you to put effects on others, which you could definitely take. For that matter, I’d even recommend allowing the Spellthief to take Personal-range effects, both spells and magic items, because that strikes me as more interesting and unique.
This will power-up the Spellthief. It’s widely regarded as a rather-weak class, so that is, in my opinion, a good thing. It’s not a huge improvement, but it does mean the Spellthief is far more likely to have target effects to steal (most enemies wear magic equipment; not every enemy has a steal-able spell up), plus the ability to grab Personal-range stuff is a good way for the Spellthief to get buffs that are usually fairly hard to get.
So talk to your DM; he may be on board with giving the Spellthief class this little boost, and that would be cool.