I am trying to create an icon in Ai. But the problem I am facing is...
I want to give a rounded stroke. Any idea how would I achieve this?
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You can't easily round the corners if you want to keep the lines as open paths with a stroke. There is no way to round a stroke on separate paths where two paths are touching. No such functionality exists. However, it's easy to do this on a closed path which is filled.
Select the stroked paths and do Object > Expand - this will convert the strokes to shapes with a fill.
Open the PathFinder and hit the Unite button. This is a boolean operation to unite the separate pieces
Select one of the Live Corner Widgets, and click and drag it.
It would be possible to retain the paths as strokes, but then you would have to draw a filled shape on top manually to make a piece that gives the illusion of a curved join. Any time you change the strokes, you'd need to manually edit this covering piece.