Hi nauna,
Use RegularExpressionValidator.
HTML
<asp:TextBox ID="txtDate" runat="server" />
<asp:RegularExpressionValidator runat="server" ControlToValidate="txtDate"
ValidationExpression="((0[1-9]|1[0-2])\/((0|1)[0-9]|2[0-9]|3[0-1])\/((19|20)\d\d))$"
ErrorMessage="Invalid date format." ForeColor="Red" />
Screenshot