We investigated local magnetic flux biasing (LFB) that induces a phase shift in superconductor circuits by locally applying a magnetic field through the superconductor loop with Josephson junctions. The arbitrary phase shift can be achieved using LFB without modifying the circuit fabrication process. To quantitatively evaluate the effects of introducing LFB for practical superconductor circuit applications, we designed a single flux quantum (SFQ) based non-destructive read-out flip-flop with complementary outputs (NDROC) and a delay flip-flop with complementary outputs (DFFC). The circuit area and static power consumption of the NDROC based on LFB architecture (LFB-NDROC) are approximately 67% and 36% of a conventional NDROC, respectively. The measured bias margin of the LFB-NDROC was in the range of 69%–129%. Using LFB, we were able to reduce the circuit area and power consumption for the DFFC by 67% and 83%, respectively. The measured bias margin of the DFFC with LFB was between 115% and 128%. LFB enabled us to implement a 5-to-32 SFQ decoder which comprises NDROC trees with a reduced circuit area of approximately 60% of a conventional decoder. The results obtained in this study can be applied to not just SFQ circuits but other superconductor circuits also, as they improve the area and power efficiency of such circuits.