this should work
'meta_query' => array(
array(
'key' => 'associated_artist',
'value' => get_the_ID(),
'compare' => '='
)
)
A post object field that only allows 1 selection does not store an array like a relationship does. It will only store and array if you allow multiple selections. Soe the quotes around the ID and the LIKE comparison is not required.