Here's the most basic weldig symbol I can think of.
This would be acceptable on a contract drawing per AWS D1.1-2010 clause 2.3.5.3. If a partial joint penetration weld is sufficient, substitute PJP in the tail and add the joint penetration requirement below the reference line, i.e., (1/8) for example, if the joint is welded from the arrow side. Then it is left to the contractor to determine the actual joint detail.
Since the joint in the photograph is tube to tube it is a T, Y, or K joint, both having the same diameter. A fillet weld all around it ain't. A bevel groove preparation would work. The reinforcing fillets in the heel or toe would not be the basis of rejecting the completed weld.
Best regards - Al