As the scale of electronic devices shrinks, "electronic textiles" (e-textiles) will make possible a wide variety of novel applications which are currently unfeasible. Due to the wearability concerns, low-power techniques are critical for e-textile applications. In this paper, we address the issue of the energy-aware routing for e-textile platforms and propose an efficient algorithm to solve it. The platform we consider consists of dedicated components for e-textiles, including computational modules, dedicated transmission lines and thin-film batteries on fiber substrates. Furthermore, we derive an analytical upper bound for the achievable number of jobs completed over all possible routing strategies. From a practical standpoint, for the Advanced Encryption Standard (AES) cipher, the routing technique we propose achieves about fifty percent of this analytical upper bound. Moreover, compared to the non-energy-aware counterpart, our routing technique increases the number of encryption jobs completed by one order of magnitude.