I chose to use "artifact" instead of "equipment" because otherwise the card would read like this

You may pay the equip cost of any equipment on the battlefield to equip that equipment to Temporal Thief Homura.

Equip much?

That doesn't look like a real word any more.

Alexander, I believe the proper templating would use "attach" rather than "equip", so it'd look something like:

"You may activate the Equip ability of any Equipment on the battlefield and attach that card to Temporal Thief Homura."

Or essentially what you have:

"You may pay the Equip cost of any Equipment on the battlefield to attach that card to Temporal Thief Homura."

Also, I'm not being snarky, but did you mean for her to be a Rouge or a Rogue? It's an easy mistake to make, and I just don't know if being a "rouge" means something in the context of Madoka Magi-ka.

It'd actually be best written as an activated ability, with a colon:

> Pay the equip cost of an Equipment on the battlefield: Attach that Equipment to ~.

Note that this doesn't target (because you can't target in costs), it doesn't refer to the equipment as a "card" (because it might not be thanks to Prototype Portal), it uses "attach" as the imperative verb, capitalises "Equipment" as it's a subtype, and doesn't capitalise "equip" because that's only capitalised at the start of a line or sentence.

Alex C, Rules Guru to the rescue. ;)

On a somewhat depressing note, you can take guidance from Piracy here.

"You may activate equip abilities of Equipment you don't control. Choose only CARDNAME as the target of abilities activated this way."

This makes clear that it's the actual equip ability you're using, rather than some other ability with the same cost, so it allows the sorcery-speed restriction to remain implicit instead of being spelled out in more rules text. It also avoids the potential confusion of "This equipment somehow lost its equip ability. Does that mean I can take it for or does the 'equip cost' resolve to an unpayable blank cost {} like on Evermind?"

@M_Houlding Thanks for catching my spelling mistake. That was supposed to be Rogue not Rouge.