Bigquery array of STRINGs to array of INTs

I'm trying to pull an array of INT64 s in BigQuery standard SQL from a column which is a long string of numbers separated by commas (for example, 2013,1625,1297,7634). I can pull an array of strings easily with:

SELECT
  SPLIT(string_col,",")
FROM
  table

However, I want to return an array of INT64 s, not an array of strings. How can I do that? I've tried

CAST(SPLIT(string_col,",") AS ARRAY<INT64>) 

but that doesn't work.