Silence says it can be cast on a creature, object, or point in space.
Spiritual Weapon definitely isn't a creature or point in space, so is it an object?
I lean towards no.
A wall of force is an actual object that is made of force, but not every thing that is made of force is an object. As an example magic missile does not create objects.
An object is something that can be affect normally and manipulated normally. That wall of force as an example has hardness and hit points. All objects do. Spiritual Weapon has neither.
Hardness: Each object has hardness—a number that represents how well it resists damage. When an object is damaged, subtract its hardness from the damage. Only damage in excess of its hardness is deducted from the object's hit points (see Table: Common Armor, Weapon, and Shield Hardness and Hit Points, Table: Substance Hardness and Hit Points, and Table: Object Hardness and Hit Points).
Hit Points: An object's hit point total depends on what it is made of and how big it is (see Table: Common Armor, Weapon, and Shield Hardness and Hit Points, Table: Substance Hardness and Hit Points, and Table: Object Hardness and Hit Points). Objects that take damage equal to or greater than half their total hit points gain the broken condition (see Conditions). When an object's hit points reach 0, it's ruined.
A wall of force creates an invisible wall of pure force. The wall cannot move and is not easily destroyed. A wall of force is immune to dispel magic, although a mage's disjunction can still dispel it. A wall of force can be damaged by spells as normal, except for disintegrate, which automatically destroys it. It can be damaged by weapons and supernatural abilities, but a wall of force has hardness 30 and a number of hit points equal to 20 per caster level. Contact with a sphere of annihilation or rod of cancellation instantly destroys a wall of force.
As you can see the wall of force has hit points and hardness, and qualifies as an actual object.
Besides casting a spell on an animated 'object' that automatically follows someone around where very little can be done about it feels wrong :)
Actually, now that I read it again, I see that the spell itself refers to the weapon as an object: "A spiritual weapon's AC against touch attacks is 12 (10 + size bonus for Tiny object)."
That is not telling you the weapon is an object. It is just telling you how the AC was calculated since it is the same size as a tiny object.
Given the above, I'd say yes. Even it were not allowed, it would be a simple workaround, so I'd allow it anyway.
An object is something that can be affect normally and manipulated normally.That makes sense, but does it have any RAW support?
No, but it is how spells work. Even if you dont like that answer I did quote that objects have hardness and hit points. RAW does not say some objects have hardness and hit points, so for SW to qualify it would need a specific rules exception. It does not have one..