An apparatus and method for splicing tapes dispensed from a tape dispenser. According to one embodiment, a first, running or unwinding roll of tape is provided with a first splicing element secured to its trailing end portion. A second, stationary or standby roll of tape is provided with a second splicing element secured to its leading end portion. The second splicing element comprises a body made of a self-supporting material and formed with at least one aperture sized to receive the tape from the first roll. While tape is being dispensed from the first roll, the running tape is inserted into the aperture of the second splicing element. When the first roll of tape becomes depleted, the first splicing element engages the second splicing element, thereby splicing the leading end portion of the second tape roll to the trailing end portion of the first tape roll.