import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.time.LocalDateTime;
import java.time.format.DateTimeFormatter;
import java.util.Locale;

class Main {
    public static void main(String[] args) throws ParseException {
        DateTimeFormatter parser = DateTimeFormatter.ofPattern("yyyy-MM-dd'T'HH:mm:ss", new Locale("ar"));
        LocalDateTime ldt = LocalDateTime.parse("2013-01-20T16:48:43", parser);
        System.out.println(ldt);

        // Alternatively, as suggested by Basil Bourque
        parser = DateTimeFormatter.ISO_LOCAL_DATE_TIME.withLocale(new Locale("ar"));
        System.out.println(LocalDateTime.parse("2013-01-20T16:48:43", parser));

        // Your parser
        final SimpleDateFormat format = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss", new Locale("ar"));
        System.out.println(format.parse("2013-01-20T16:48:43"));
    }
}