Is There any RNN method used for Object detection
Yes, there have been many attempts, but perhaps the most noteable one is the approach described in the paper of Andrej Karpathy and  Li Fei-Fei where they connect a CNN and RNN in series (CNN over image region + bidirectional RNN + Multimodal RNN) and use this for labeling a scene with a whole sentence. Though, this one is more than just object detection as it leverages a data set of scenes and their descriptions to generate natural language descriptions of new unseen images.

Another example is Ming Liang and Xiaolin Hu's approche where they mix a CNN with an RNN and use this architecture for better object detection. As Ming and Xiaolin explained in their paper (linked above), the RNN is used to improve the CNN:


  A prominent difference is that CNN is typically a feed-forward architecture while in the visual system recurrent connections are abundant. Inspired by this fact, we propose a recurrent CNN (RCNN) for object recognition by incorporating recurrent connections into each convolutional layer.