The human brain encodes stimuli from the environment into representations that form a sensory perception of the world. Despite recent advances in understanding visual and auditory perception, olfaction remains an under-explored topic in the machine learning community due to the lack of large-scale datasets annotated with labels related to human olfactory perception. In this work, we ask the question of whether transformer models trained on chemical structures encode representations that are aligned with human olfactory perception, i.e., \emph{can transformers smell like humans}? We demonstrate, by means of three analyses, that representations encoded from transformers pre-trained on general chemical structures are highly aligned with human olfactory perception. We use 5 different datasets and 3 different types of perceptual representations to show that the representations encoded by transformer models are able to predict 1) labels associated with odorants provided by experts; 2) ratings provided by human participants with respect to pre-defined descriptors; 3) similarity ratings between odorants provided by human participants. Finally, we also evaluate the extent to which this alignment is associated with chemical features of odorants known to be relevant for olfactory perception.