Yes, ticks can live in carpet. In fact, carpet is a good nest place for ticks to lay their eggs. Ticks typically prefer to lay their eggs on soil, branches, or leaves but if there is a suitable host inside of your house they can lay their eggs on carpet and live in carpet. You will rarely see a tick infestation in your house since they are relatively easy to get rid of with pesticides, but it does happen if you’re not careful or a clean person.