How to select the Date Picker In Selenium WebDriver

DatePicker are not Select element. What your doing in your code is wrong.

Datepicker are in fact table with set of rows and columns.To select a date you just have to navigate to the cell where our desired date is present.

So your code should be like this:

WebElement dateWidget = driver.findElement(your locator);
List<WebElement> columns=dateWidget.findElements(By.tagName("td"));

for (WebElement cell: columns){
   //Select 13th Date 
   if (cell.getText().equals("13")){
      cell.findElement(By.linkText("13")).click();
      break;
 }