Can a diocesan priest become a missionary? Can a diocesan priest become a missionary? Can he demand it? Does he need consent from his bishop (I know he can become a religious without consent)?.
Can a diocesan priest become a missionary?
The short answer is yes.
A diocesan priest actually does not need the bishop’s permission to enter a Religious Order as it is a higher state of perfection. A bishop may however, and reasonably so, delay letting him go, in order to test his vocation.
On the contrary a diocesan priest may become a missionary, but must obtain permission from his own diocesan bishop. This sort of permission is also required when other diocesan bishops request help from other dioceses for priests to help in their diocese. Even Rome needs the permission of the local bishop when it requests priests to work at the Vatican. I have never heard of any bishop refusing the request of a particular priest to help out at the Vatican which is usually a 5 year term and is often renewed once, if the priest in question is comfortable with his work.
Here in the Archdiocese of Vancouver, I have known a number of priests to work in the missions, sometimes at their own request and at other times at the request of Rome.
Fr. Stanley Francis Rother of the Archdiocese of Oklahoma City is an example of a diocesan priest who not only worked as a missionary in Guatemala but is now well on his way to be beatified as a martyr.

Stanley Francis Rother(March 27, 1935 – July 28, 1981) was an American Roman Catholic priest from Oklahoma who was murdered in Guatemala. Ordained as a priest for the Archdiocese of Oklahoma City in 1963, he held several parish assignments there until 1968 when he was assigned as a missionary priest to Guatemala where he was murdered in 1981 in his Guatemalan mission rectory.
Guatemalan pastor
So that Rother could be in closer touch with his congregation, he set out to work to learn Spanish and the Tz’utujil language which was an unwritten and indigenous language that the missionary Ramón Carlín once recorded. He served in Santiago Atitlán from 1968 until his death. He supported a radio station located on the mission property, which transmitted daily lessons in language and mathematics. In 1973 he noted with pride in a letter: &quot;I am now preaching in Tz'utuhil.&quot; During that time, in addition to his pastoral duties, he translated the New Testament into Tz'utujil and began the regular celebration of the Mass in Tz'utujil. In the late 1960s, Rother founded in Panabaj a small hospital, dubbed as the &quot;Hospitalito&quot;; Father Carlín served as a collaborator in this project.
By 1975, Rother had become the de facto leader of the Oklahoma-sponsored mission effort in Guatemala as other religious and lay supporters rotated out of the program. He was a highly recognizable figure in the community, owing to his light complexion as well as his habit of smoking tobacco in a pipe. Since there was not a Tz'utujil name equivalent to &quot;Stanley,&quot; the people of Rother's mission affectionately called him &quot;Padre Apla's,&quot; translated as &quot;Father Francis,&quot; a nod to his middle name.