Generally RadGridView supports selection out-of-the-box. However, in your case, you want to perform this action using a control placed in CellTemplate of the column(the TextBox). If you click on the cell which contains the control, you will actually click in the TextBox instead of GridViewRow/GridViewCell, so RadGridView's selection logic will not work.
For more information about CellTemplate
you can check the Setting CellTemplate and CellEditTemplate documentation article.
I hope this helps.
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