WPF's DataGrid uses a TextBlock for the cell when the row is not in edit mode. When it is in edit mode, a TextBox is used. Neither control has a property that affects the vertical alignment within the control, but using a style you could set the VerticalAlignment of the TextBox itself to be center-aligned. This might cause undesired side effects though since there will now be areas of the edited cell not covered by the TextBox.
<DataGridTextColumn ...>
    <DataGridTextColumn.EditingElementStyle>
        <Style TargetType="{x:Type TextBox}">
            <Setter Property="VerticalAlignment" Value="Center" />
        </Style>
    </DataGridTextColumn.EditingElementStyle>
</DataGridTextColumn>