From CS rulebook,duplicates has no trait.

Can I give traits to a duplicate?

With Copper Link, technically yes. It is a card in play.

Huh, that answer surprises me. I suppose I had always taken "Duplicates have no text, titles,traits, or crests," to mean that they never have any of those things… though I can see how it might be read that they don't have those things when played. Hmm.

In that case,the duplicate has the trait,or it's still a card w/o any trait because of the words in the rulebook?

"Do not have" and "cannot have" are the the same. There is nothing that says a duplicate cannot gain a trait. The only thing that Copper Link cares about is whether the card it chooses is in play (making duplicates and House cards legal targets). There's nothing stopping the duplicate from holding a gained trait. And there is nothing stopping dupes from interacting with "card in play" effects. For instance, people use Wintertime Marauders to discard dupes all the time.

Think of "token characters" like Reinforcements. The effects put the events into play as characters with certain defined STR, keywords, and icons. Can those token characters gain/lose icons, keywords, and STR from other effects despite being defined by the effect that created them? Sure. How is that any different than the dupe being put into play as a card without text, title, traits, or crest?