Galaxies grow through both internal and external processes. In about 10% of nearby red galaxies with little star formation, gas and stars are counter-rotating, demonstrating the importance of external gas acquisition in these galaxies. However, systematic studies of such phenomena in blue, star-forming galaxies are rare, leaving uncertain the role of external gas acquisition in driving evolution of blue galaxies. Here, based on new measurements with integral field spectroscopy of a large representative galaxy sample, we find an appreciable fraction of counter-rotators among blue galaxies (9 out of 489 galaxies). The central regions of blue counter-rotators show younger stellar populations and more intense, ongoing star formation than their outer parts, indicating ongoing growth of the central regions. The result offers observational evidence that the acquisition of external gas in blue galaxies is possible; the interaction with pre-existing gas funnels the gas into nuclear regions (<1 kpc) to form new stars.