A reversible cellular automaton (RCA) is a computing model having a property analogous to physical reversibility. We investigate the problem of finding simple RCAs in which any circuit composed of rotary elements (REs) can be embedded. Since an RE is known to be a universal reversible logic element, such RCAs are also universal in this respect. In this paper, after giving a survey of known results on RE and its implementation in RCAs, we propose a new RCA model in which REs and some signal routing elements can be embedded. The new model has a simpler local transition function (in the sense it is described by fewer rules) than the previous one, though the number of states is the same. In addition, the patterns realizing an RE and signal routing elements are smaller than those of the previous model.