Add an empty column to Spark DataFrame

All you need here is importing StringType and using lit and cast:

from pyspark.sql.types import StringType
from pyspark.sql.functions import lit

new_df = old_df.withColumn('new_column', lit(None).cast(StringType()))

A full example:

df = sc.parallelize([row(1, "2"), row(2, "3")]).toDF()
df.printSchema()
# root
#  |-- foo: long (nullable = true)
#  |-- bar: string (nullable = true)

new_df = df.withColumn('new_column', lit(None).cast(StringType()))

new_df.printSchema()
# root
#  |-- foo: long (nullable = true)
#  |-- bar: string (nullable = true)
#  |-- new_column: string (nullable = true)

new_df.show()
# +---+---+----------+
# |foo|bar|new_column|
# +---+---+----------+
# |  1|  2|      null|
# |  2|  3|      null|
# +---+---+----------+

A Scala equivalent can be found here: Create new Dataframe with empty/null field values