Selecting attributes that contain "%"-symbol in Field Calculator

From the last answer to How do I escape a percentage sign in T-SQL? this is working with my data that is in a file geodatabase:

textfield LIKE '%|%%' ESCAPE '|'

The query might be different depending on your data source.

You can use python with da.SearchCursor to look for %-signs and select by objectid of the rows matching:

import arcpy
layer = 'ak_riks'
field_to_search_in = 'textfield'
search_for = '%'

oidfield = arcpy.Describe(layer).OIDFieldName
oids_to_select = tuple([oid for oid, phrase in arcpy.da.SearchCursor(layer, ['OID@', field_to_search_in]) if search_for in phrase])

sql = """{0} IN{1}""".format(oidfield, oids_to_select)
arcpy.SelectLayerByAttribute_management(in_layer_or_view=layer, where_clause=sql)