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Can I run Qwen3-4B-Base on an RTX 4090?

Yes

Its published weights (8.04 GB) fit in the 21.6 GB an RTX 4090 can use, with room for ≈ 32K tokens of context.

Full analysis of Qwen3-4B-Base Everything that runs on RTX 4090 Get the weights on Hugging Face
hf download Qwen/Qwen3-4B-Base

Files and context on RTX 4090

Each file of Qwen3-4B-Base (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.

FileSizeOn RTX 4090 Context (16-bit)Context (8-bit)
As published8.04 GBFits32K32K
4-bit (estimate)2.26 GBFits32K32K

Qwen3-4B-Base 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.