The optical in-phase and quadrature modulator (IQM) is typically utilized as an optical single-sideband (SSB) transmitter for its simple structure and low cost. It requires the modulator biases to be slightly offset for generating the optical carrier. However, this poses significant challenges in the bias control circuits, as most off-the-shelf automatic bias control (ABC) modules are designed to stabilize the IQM at its carrier suppression point for coherent optical communication. In this paper, a novel arbitrary ABC scheme is proposed to stabilize the carrier-to-signal power ratio (CSPR) of an optical SSB signal over long-term operation. This scheme uses SSB rather than double-sideband (DSB) sinusoidal signals as the dither signals. It does not violate the minimum phase condition, thus avoiding performance penalties compared to the conventional ABC scheme in which the DSB dither signal is used. We also develop a closed-form expression to reveal the relationship between the control parameter in the ABC algorithm and the CSPR of the optical SSB signal. By this means, the optical SSB transmitter can automatically adjust its bias voltages and stabilize them at a given CSPR value. The experimental results with ∼80 Gb/s optical SSB signal show that our proposed ABC scheme is effective in stabilizing the bias of the IQM at any point and maintains the CSPR value of the optical SSB signal over hours. It is also shown that the proposed method leads to 1 dB improvement in the receiver sensitivity compared with the traditional ABC technique.