This paper investigates the information-theoretic limits of the additive white Gaussian noise (AWGN) energy-harvesting (EH) channel in the finite blocklength regime. The EH process is characterized by a sequence of i.i.d. random variables with finite variances. We use the save-and-transmit strategy proposed by Ozel and Ulukus (2012) together with Shannon's non-asymptotic achievability bound to obtain a lower bound on the achievable rate for the AWGN EH channel. The first-order term of the lower bound on the achievable rate is equal to C and the second-order (backoff from capacity) term is proportional to equation, where n denotes the blocklength and C denotes the capacity of the EH channel, which is the same as the capacity without the EH constraints. The constant of proportionality of the backoff term is found and qualitative interpretations are provided.