BDO Canon Awakening Weapon is highly desired because you can trade it in for a Narchillan Awakening Weapon.
Canon Awakening Weapon is given as a reward during the Awakening Weapon quest line.
To view this quest line, Press O key and Main tab. Look for a section titled “[Lv. 56] *class* New Power”
It is located toward the middle or end of the Awakening quest line, right before you have a tutorial and have to demonstrate a few Awakening skills.
Rumor: It has been reported that you can talk to your quest NPC, if you previously deleted your Canon Weapon to obtain another. I have not confirmed this yet.

Canon Awakening Weapon
You obtain the Canon Awakening Weapon via the Awakening quest line, different for each class.
Below is a list of quests that give the Canon Awakening Weapon: