By inevitably reducing the transistor size of the semiconductors to the nano level, the current transistor-based technology has faced many challenges such as high chip temperature, reduced operating circuit accuracy, high current leakage, high power, etc. Therefore, several studies have been conducted to find an appropriate substitution for these circuits. One of the most important results of these studies is Quantum-Dot Cellular Automata (QCA), proposed as a possible replacement for conventional circuits. With the increasing volume of circuits, the complexity of designing and manufacturing circuits and the complexity of producing suitable test vectors for them increases, so producing and performing complete test operations on large circuits is very time-consuming and costly. Therefore, it is very important to find ways to produce circuits that can perform the test operation inside the circuit. This article gives a new design for testing circuits based on QCA to minimize overall consumption space. In this design, a linear transmission register circuit is provided to produce test patterns, and a serial signature register is presented to check the circuit's response to the test patterns. In designing these circuits, the minimum consumption of cells has been employed. Therefore, applying this design in QCA circuits increases the testability of circuits and self-test circuits. Besides, due to the minimum cell number used in the design of these circuits, the occupied area is reduced. The simulation outcomes illustrated that the suggested technique, compared to similar designs, gained significant improvement in terms of consumed area and cell.