RNN language models have achieved state-of-the-art results on various tasks, but what exactly they are representing about syntax is as yet unclear. Here we investigate whether RNN language models learn humanlike word order preferences in syntactic alternations. We collect language model surprisal scores for controlled sentence stimuli exhibiting major syntactic alternations in English: heavy NP shift, particle shift, the dative alternation, and the genitive alternation. We show that RNN language models reproduce human preferences in these alternations based on NP length, animacy, and definiteness. We collect human acceptability ratings for our stimuli, in the first acceptability judgment experiment directly manipulating the predictors of syntactic alternations. We show that the RNNs' performance is similar to the human acceptability ratings and is not matched by an n-gram baseline model. Our results show that RNNs learn the abstract features of weight, animacy, and definiteness which underlie soft constraints on syntactic alternations.