You would need to use dynamic SQL. For example:
DECLARE @file_name varchar(500)
DECLARE @sql varchar(8000)
SET @file_name = 'F:\HorseDb\659620.csv'
SET @sql = '
BULK INSERT dbo.HorseRacingMasterTable
FROM ''' +@file_name + '''
WITH
(
FIRSTROW = 2,
FIELDTERMINATOR = '','',
ROWTERMINATOR = ''\n''
)'
--PRINT @sql
EXEC(@sql)