Loop: IF cell is not blank then output adjacent cell

I'm a VBA newbie so i'm cobbling together pieces of code I've picked up online. I have the below which i think is close but rather than 'my text' i would like to repeat whatever is in the adjacent cell in column A. However, if there is already a value present in cell B, then don't do anything.

Sub Check()
    Dim rng As Range
    Dim i As Long

    'Set the range in column A you want to loop through
    Set rng = Range("A1:A100")
    For Each cell In rng
        'test if cell is empty
        If cell.Value <> "" Then
            'write to adjacent cell
            cell.Offset(0, 1).Value = "My Text"
        End If
    Next
End Sub

Help most appreciated.

Never got back to you AlphaFrog. Apologies. This is perfect - Thank you.