Electrical edge joint of a stacked high-temperature superconducting (HTS) conductor is explored for electrical joints for a demountable HTS toroidal field coil. Demountable coils would be very useful in small tokamak plasma-facing component-test machines, such as Vulcan. The demountable concept consists of forcing together the edges of stacked HTS conductor embedded in a conductive or a structural material. Numerical evaluation showed that inserting an indium film between joint surfaces or plating copper layer on joint surfaces could prevent joint resistance from increasing due to misalignment of the contact surface and would provide a compliant layer between joints. Joint resistance of the edge joint can become smaller than that of electrical lap joint when the number of the stacked HTS tape is large. We carried out a testing program of the edge joint of a stacked YBCO conductor within a copper jacket. The HTS cable has a critical current of 1600 A at 77 K in self field. The experimental results showed that joint resistance in the edge joint was higher than expectation, as was irreproducible. One potential reason for the degradation of HTS material is the damage to the tape edge in preparation of the joint region due to milling. Another potential reason was low accuracy of fabrication of joint surface, the joint surface were not parallel to another one. The joint resistance will be reduced by sophistication of fabrication process for the joint surface.