You would use a combination of the functions:
pyspark.sql.functions.from_unixtime(timestamp, format='yyyy-MM-dd HH:mm:ss')
(documentation) and
pyspark.sql.functions.unix_timestamp(timestamp=None, format='yyyy-MM-dd HH:mm:ss')
(documentation)
from pyspark.sql.types import *
from pyspark.sql.functions import unix_timestamp, from_unixtime
df = spark.createDataFrame(["6/3/2019 5:06:00 AM"], StringType()).toDF("ts_string")
# convert to timestamp type
df1 = df.select(from_unixtime(unix_timestamp('ts_string', 'MM/dd/yyyy hh:mm:ss a')).cast(TimestampType()).alias("timestamp"))
# change timestamp format
df2 = df1.select(from_unixtime(unix_timestamp('timestamp', 'MM-dd-yyyy hh:mm:ss')).alias("timestamp2"))
# all together
df3 = df.select(
'ts_string',
from_unixtime(unix_timestamp('ts_string', 'MM/dd/yyyy hh:mm:ss a')).cast(TimestampType()).alias("timestamp"),
from_unixtime(unix_timestamp(from_unixtime(unix_timestamp('ts_string', 'MM/dd/yyyy hh:mm:ss a')).cast(TimestampType()), 'MM-dd-yyyy hh:mm:ss')).alias("timestamp2")
)