In this card game, you have a hand of 10 cards where you try to order them by replacement. On your turn, you draw a card, switch it with one in your hand, and discard the other one. You can use the top card of the discard pile.
Seems you're thinking of Rack-O.
In Rack-O, you have a deck of 40-60 uniquely numbered cards, and start by filling your 10-card rack with them in a random order. You then take turns replacing cards in your rack with either the top card of the discard pile or deck, and the first player to get their cards in ascending order wins. If I remember correctly from playing it, you can't rearrange the cards in your rack either.