Of course you can!!!!   It is enough to grab a taxi anywhere in Barcelona, say destination and pay at the end. Conversely, you will find taxis in Montjuic as well as you can easily call for a taxi there.   Taxi fares are the same. Montjuic mountain could be different because there are a lot of facilities (museums, stadiums and so) and no buildings for houses.... but definitely the same for taxis.   In this thread you have more information about fares