Try this, it should work:
> from pyspark.sql.functions import unix_timestamp
> df = spark.createDataFrame([("11/25/1991",), ("11/24/1991",), ("11/30/1991",)], ['date_str'])
> df2 = df.select('date_str', from_unixtime(unix_timestamp('date_str', 'MM/dd/yyy')).alias('date'))
DataFrame[date_str: string, date: timestamp]
> df2.show()
+----------+--------------------+
| date_str| date|
+----------+--------------------+
|11/25/1991|1991-11-25 00:00:...|
|11/24/1991|1991-11-24 00:00:...|
|11/30/1991|1991-11-30 00:00:...|
+----------+--------------------+