You can achieve your goal in many different way. If you want you can read delete operations from sql server transaction log, but you will "loose" it after each transaction log backup if you are in full recovery model. In simple recovery model you can not control the transaction log contents.
To find delete operations for a particular table you can use the following query:
DECLARE @MonitoredTable sysname
SET @MonitoredTable = 'YouTable'
SELECT
u.[name] AS UserName
, l.[Begin Time] AS TransactionStartTime
FROM
fn_dblog(NULL, NULL) l
INNER JOIN
(
SELECT
[Transaction ID]
FROM
fn_dblog(NULL, NULL)
WHERE
AllocUnitName LIKE @MonitoredTable + '%'
AND
Operation = 'LOP_DELETE_ROWS'
) deletes
ON deletes.[Transaction ID] = l.[Transaction ID]
INNER JOIN
sysusers u
ON u.[sid] = l.[Transaction SID]
Another approach you can use is to write an "audit trigger" or you can use directly sql server auditing features/Sql server extended events as well explained in this Apex webpage:
SQL Server database auditing techniques
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