The connection between the widget and the scrollbar goes both ways. The scrollbar needs to be expanded vertically so that it has the same height as the widget.
text = tk.Text(parent)
text.pack(side="left")
scroll_y = tk.Scrollbar(parent, orient="vertical", command=text.yview)
scroll_y.pack(side="left", expand=True, fill="y")
text.configure(yscrollcommand=scroll_y.set)