Generic object detection has achieved significant progress in recent years. However, oriented object detection in aerial images is still a challenging task due to arbitrary orientation, complex backgrounds and large scale variation. Currently, the majority of oriented object detectors are anchor-based, achieving promising performance yet suffering from complicated anchor designs and imbalance between the positive and negative anchor boxes. In this work, we propose a new anchor-free model called RBA-CenterNet for oriented object detection. Specifically, we first detect the center point of each object after extracting feature of the input image. Then, we regress the rotated box parameters in other prediction branches. Considering that using only the center point of the object may hurt the detection performance, we introduce a refinement module called rotated border alignment (RBA) to integrate the border feature into the center point feature. Our experiments show that the proposed model RBA-CenterNet can achieve comparable detection performance to state-of-the-art methods.