As written in wiki article on Kalki under his bio; His primary weapon will be Ranta Maru which is weapon of Shiva and is a sword.
Also same wiki article's description says:
Kalki is an avatara of Vishnu. Avatara means "descent" and refers to a descent of the divine into the material realm of human existence. The Garuda Purana lists ten avatars, with Kalki being the tenth. He is described as the avatar who appears at the end of the Kali Yuga. He ends the darkest, degenerating and chaotic stage of the Kali Yuga (period) to remove adharma and ushers in the Satya Yuga, while riding a white horse with a fiery sword. He restarts a new cycle of time. He is described as a Brahmin warrior in the Puranas.
Also in Kalki Purana, it is mentioned that after his Guru suggestion Lord Kalki starts worshiping Lord Shiva and Lord Shiva blesses him 3 things horse, a parrot and a sword.
This horse was manifested from Garuda, and it can go anywhere at
will and assume many different forms. Here also is a parrot that knows
everything—past, present, and future. I would like to offer You both the
horse and the parrot and so please accept them
By the influence of this horse and parrot, the people of the world will
know You as a learned scholar of all scriptures who is a master of the art
of releasing arrows, and thus the conqueror of all.
I would also like to present You this sharp, strong sword and so please
accept it. The handle of this sword is bedecked with jewels, and it is
extremely powerful. As such, this sword will help You to reduce the heavy
burden of the earth.
Reference Link : Kalki Purana