I think yes
You may escape from Bree, and be allowed to go forward while the Sun
is up; but you won’t go far. They will come on you in the wild, in
some dark place where there is no help. Do you wish them to find you?
They are terrible!’ The hobbits looked at him, and saw with surprise
that his face was drawn as if with pain, and his hands clenched the
arms of his chair. The room was very quiet and still, and the light
seemed to have grown dim. For a while he sat with unseeing eyes as if
walking in distant memory or listening to sounds in the Night far
away. ‘There!’ he cried after a moment, drawing his hand across his
brow. ‘Perhaps I know more about these pursuers than you do. You fear
them, but you do not fear them enough, yet. Tomorrow you will have to
escape, if you can. Strider can take you by paths that are seldom
trodden. Will you have him?’
FotR, Chapter 10 - Strider
He does not say's it openly, but I think his body language expresses that he has very unpleasant memoires about the riders, and that he fears a close encounter with them. Normally Aragorn can perfectly control and conceal his fear, but now he can use it to his advantage, presenting the hobbits that the Nine are not to be taken lightly.
And also in Book II, Ch 4 - A journey in the dark
‘The road that I speak of leads to the Mines of Moria,’ said Gandalf.
Only Gimli lifted up his head; a smouldering fire was in his eyes. On
all the others a dread fell at the mention of that name. Even to the
hobbits it was a legend of vague fear. ‘The road may lead to Moria,
but how can we hope that it will lead through Moria?’ said Aragorn
‘I too once passed the Dimrill Gate,’ said Aragorn quietly; ‘but though I
also came out again, the memory is very evil. I do not wish to enter Moria a
I will follow your lead now – if
this last warning does not move you. It is not of the Ring, nor of us others that
I am thinking now, but of you, Gandalf. And I say to you: if you pass the
doors of Moria, beware!’
Arguably in this case Aragorn expresses two different kind of fear: He fears Moria for himself, and he has a 'higher order fear' of losing his old friend, teacher and advisor, Gandalf.
And look at this: (Ch 10- The Breaking of the fellowship)
‘The day has come at last,’ he said: ‘the day of choice which we have
long delayed. What shall now become of our Company that has travelled
so far in fellowship? Shall we turn west with Boromir and go to the
wars of Gondor; or turn east to the Fear and Shadow; or shall we break
our fellowship and go this way and that as each may choose? Whatever
we do must be done soon.
It seems to me that Aragorn is here (and in the previous chapter) afraid of making the decision. He knows that the decision must be made, and that it would be irreversible and have decisive consequences, and although he had prepared for these times in his whole adult life, he still fears and tries to push the responsibility on Frodo. He had not expected to become leader so soon, and fears that he is not as wise as Gandalf, so he tarries, and that almost leads to catastrophe.
Aragorn feels many fears: The fear of the guts when he looks forward to encountering things that made him suffer in the past, the fear of the heart when he dreads the loss of his friends, and the fear of the mind when he is suddenly beset with enormous responsibility, and fears that he would turn out an unworthy leader and fall short of his high destiny.
The reason that the reader notices this rarely is twofold: Tolkien scarsely uses his POV, we see him through the eyes of the hobbits, Gimli and even Ioreth, but we never hear his internal monologues. And since he knows that his expressed fear would disheart his companions and lead him to decisions that further the cause of Sauron, he almost never tells them or lets them influence his deeds. We only see his fears when he is conversing with his most trusted friends and when he uses it as a tool to disaude others from foolish decisions.
Scanning further, I have found another instance when Aragorn actually admits fear:
‘Why are you waiting? What is the matter with you?’ said Gimli in a
hissing whisper. ‘Legolas is right,’ said Aragorn quietly. ‘We may not
shoot an old man so, at unawares and unchallenged, whatever fear or
doubt be on us. Watch and wait!’
Two Towers, Ch 5 - The White Rider
This is again a different kind of fear. All the previous instances originate from Aragorns superior knowledge: (compared to that of the hobbits or avarage men) Having been to Imlad Morgul he knows the true nature of the Black Riders, knowing Gandalf better than any living man, he knows that the Wizard is not as inviolable as the hobbits imagine, knowing geography and the ways of the enemy he knows that if they go to Gondor, they will have no second chance to try ro get into Mordor...
Now he does not understand: They have lost the hobbits, the signs are puzzling even to his Ranger tracker-skills, a mysterious old man chased away their horses and is now approaching, he and Legolas feel some quer foreboding in the Forest... It is a great feat of courage and self-control that he does not let their insecurities burst out in violence.