In Atacama Large Millimeter/submillimeter Array (ALMA) commissioning and science verification we have conducted a series of experiments of a novel phase calibration scheme for Atacama Compact Array (ACA). In this scheme water vapor radiometers (WVRs) devoted to measurements of tropospheric water vapor content are attached to ACA's four total-power array (TP Array) antennas surrounding the 7 m dish interferometer array (7 m Array). The excess path length (EPL) due to the water vapor variations aloft is fitted to a simple two-dimensional slope using WVR measurements. Interferometric phase fluctuations for each baseline of the 7 m Array are obtained from differences of EPL inferred from the two-dimensional slope and subtracted from the interferometric phases. In the experiments we used nine ALMA 12-m antennas. Eight of them were closely located in a 70-m square region, forming a compact array like ACA. We supposed the most four outsiders to be the TP Array while the inner 4 antennas were supposed to be the 7 m Array, so that this phase correction scheme (planar-fit) was tested and compared with the WVR phase correction. We estimated residual root-mean-square (RMS) phases for 17- to 41-m baselines after the planar-fit phase correction, and found that this scheme reduces the RMS phase to a 70 - 90 % level. The planar-fit phase correction was proved to be promising for ACA, and how high or low PWV this scheme effectively works in ACA is an important item to be clarified.