dense_rank in sql partition by id and session id but ordered by timestamp

I have a table as following:

User ID Session ID Timestamp
100 7e938c4437a0 1:30:30
100 7e938c4437a0 1:30:33
100 c1fcfd8b1a25 2:40:00
100 7b5e86d91103 3:20:00
200 bda6c8743671 2:20:00
200 bda6c8743671 2:25:00
200 aac5d66421a0 3:10:00
200 aac5d66421a0 3:11:00

I am trying to rank each session_id for by user_id, sequenced(ordered by) timestamp. I want something like the second table.

I am doing the following but it does not order by timestamp:

dense_rank() over (partition by user_id order by session_id) as visit_number


it outputs in wrong order and when I add timestamp in the order by it behaves like a row_number() function.

Below is what I am really looking for to get as a result:

User ID Session ID Timestamp Rank
100 7e938c4437a0 1:30:30 1
100 7e938c4437a0 1:30:33 1
100 c1fcfd8b1a25 2:40:00 2
100 7b5e86d91103 3:20:00 3
200 bda6c8743671 2:20:00 1
200 bda6c8743671 2:25:00 1
200 aac5d66421a0 3:10:00 2
200 aac5d66421a0 3:11:00 2

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