I went through the documenation @marc_s linked to, and found the usage of DATAFILETYPE = widechar.
I then went ahead and tried it with my UTF-8 csv file, but it didn't work, giving me the error:
[...] the data file does not have a Unicode signature
I then re-saved my csv file with Notepad's Unicode format, retried the import, and voila, success.
My full script (I'm using SQL Server 2017):
BULK INSERT [my_table]
FROM 'C:\path\to\file.csv'
WITH
(
FORMAT = 'CSV',
FIRSTROW = 2,
FIELDTERMINATOR = ',',
KEEPIDENTITY, -- remove it if you don't want identity to be kept
ROWTERMINATOR = '\n',
DATAFILETYPE = 'widechar',
ERRORFILE = 'C:\path\to\file_err.csv',
KEEPNULLS,
TABLOCK
)
Note: regarding KEEPNULS, read this question (e.g, if you have NULLs in your file, replace them with an empty string).