Yes
If you read the skill description from the pathfinder 1e reference document, you will notice that it says that intimidation affects "an opponent" and that their "wisdom modifier" plays a role. My conclusion would be that anything which has a wisdom modifier and is capable of comprehending your attempts at intimidation can potentially be intimidated.
The FAQ says "fearless and mindless creatures are immune to all uses of Intimidate". But I would not consider an intelligent magic item with Wis, Cha and Int scores "mindless" and (depending on its personality) it might not be "fearless" either.
The rules on intelligent magic items say that they are "Magically imbued with sentience, these items think and feel the same way characters do and should be treated as NPCs" and "Intelligent items can actually be considered creatures because they have Intelligence, Wisdom, and Charisma scores". This implies that characters should be able interact with intelligent items socially, which would also imply the usage of social skills like "intimidate" on them.
Yes, that article also says to "Treat them as constructs". And Constructs have "Immunity to all mind-affecting effects (charms, compulsions, morale effects, patterns, and phantasms)". But contrary to what the other answer claims, constructs are not necessarily "mindless". And Intimidate is not any of those "mind-affecting effects" mentioned here. You might notice that all of those examples (including "Charm and Compulsions") are magical in nature, while the intimidate skill is just the mundane application of social skills. Intimidation does not affect the mind of the target in any other way than regular words do. It uses verbal and non-verbal language to convinces the target that cooperation is the logical conclusion to avoid harm.
So in conclusion, I see no reason why it shouldn't be possible to threaten an intelligent magical item with getting broken into pieces and why it would not be appropriate to handle that situation by applying the rules for the Intimidate skill.