Can I run petitgpt on an RTX 4090?

Yes

Its published weights (499 MB) fit in the 21.6 GB an RTX 4090 can use, with room for an unknown amount of context.

hf download yqi0/petitgpt

Files and context on RTX 4090

Each file of petitgpt (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

petitgpt on other hardware

Popular models that run on RTX 4090

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.