Can I run gemma-3-27b-it-int4-awq on an RTX 3060 12 GB?

No

Even its smallest file (4-bit (estimate), 15.4 GB) is more than an RTX 3060 12 GB can hold (10.8 GB usable): it needs 2 of them.

Files and context on RTX 3060 12 GB

Each file of gemma-3-27b-it-int4-awq (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.

gemma-3-27b-it-int4-awq 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.