This paper presents an ICA-based robot audition system which estimates the reverberation time of the environment automatically by using the robot's own speech. The system is based on multi-channel semi-blind independent component analysis (MCSB-ICA), a source separation method using a microphone array that can separate user and robot speech under reverberant environments. Perception of the reverberation time (RT) is critical, because an inappropriate RT degrades separation performance and increases processing time. Unlike most previous methods that assume the RT is given in advance, our method estimates an RT by using the echo's intensity of the robot's own speech. It has three steps: speaks a sentence in a new environment, calculates the relative powers of the echoes, and estimates the RT using linear regression of them. Experimental results show that this method sets an appropriate RT for MCSB-ICA for real-world environments and that word correctness is improved by up to 6 points and processing time is reduced by up to 60%.