Yes, you can! Self-Inking stamps can be re-inked with a bottle of water-based ink or you can buy a new pad to put in your stamp.
Refill Ink for Self-Inking Stamps
Replacement Ink Pads for Self-Inking Stamps
Pre-Inked stamps can only be refilled with oil-based ink.
Refill Ink for Pre-Inked Stamps