...at least in the books.
Aragorn was silent for a moment. ‘Three days,’ he murmured, ‘and the muster of Rohan will only be begun. But I see that it cannot now be hastened.’ He looked up, and it seemed that he had made some decision; his face was less troubled. ‘Then, by your leave, lord, I must take new counsel for myself and my kindred. We must ride our own road, and no longer in secret. For me the time of stealth has passed. I will ride east by the swiftest way, and I will take the Paths of the Dead.’
‘The Paths of the Dead!’ said Théoden, and trembled. ‘Why do you speak of them?’ Éomer turned and gazed at Aragorn, and it seemed to Merry that the faces of the Riders that sat within hearing turned pale at the words. ‘If there be in truth such paths,’ said Théoden, ‘their gate is in Dunharrow; but no living man may pass it.’
‘You will do as you will, my lord Aragorn,’ said Théoden. ‘It is your doom, maybe, to tread strange paths that others dare not. This parting grieves me, and my strength is lessened by it; but now I must take the mountain-roads and delay no longer. Farewell!’
Return of the King - Passing of the Grey Company
The visit from Elrond in the movie is a creation by Peter Jackson. In the books, Aragorn is visited by Elrond's son, Elrohir who brings him a message from Elrond.
‘I bring word to you from my father: The days are short. If thou art in haste, remember the Paths of the Dead.’
In fact, Aragorn was already carrying Anduril in the books...so it seems the scene was to have Elrond at least partially involved and have another refernce to Arwen in the movie.
Any conversation between Aragorn and Theoden therefore, took place, off-screen...or Jackson just left it out entirely.