There's not enough information here to determine whether strtotime or datetime can be used directly. The format of 10/08/2013 is either August 10, 2013 or October 8, 2013 which was not specified by the OP.
If it stands for October 8, 2013, you can use strtotime or DateTime directly. If it stands for August, you must separate the date parts using explode or any similar method, and manually construct it using mktime or datetime::setdate functions.
Since the SQL date of 2013-08-10 is August 10, 2013, you'll need to do it manually by splitting the components up and using the mktime or datetime::setdate functions. If the data is already in SQL you can use the SQL functions to copy it over directly. You can look at the str_to_date
function for that. I assume you're trying to copy this over to a new property in a table; without proper DateTime datatypes in SQL you cannot properly search or sort by dates provided.