Can I run Qwen2-0.5B on an RTX 3060 12 GB?

Yes

Its published weights (988 MB) fit in the 10.8 GB an RTX 3060 12 GB can use, with room for ≈ 128K tokens of context.

hf download Qwen/Qwen2-0.5B

Files and context on RTX 3060 12 GB

Each file of Qwen2-0.5B (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.

Qwen2-0.5B on other hardware

Popular models that run on RTX 3060 12 GB

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.