Yes.  There is a spiritual gift given to some to witness to others about the Lord Jesus.  It is called the gift of evangelism.  Let’s read Ephesians 4:9-11, “(Now that he ascended, what is it but that he also descended first into the lower parts of the earth? He that descended is the same also that ascended up far above all heavens, that he might fill all things.) And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers.”  This portion speaks of the resurrected Christ giving gifts to the Church, “For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ: Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ: That we henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive; But speaking the truth in love, may grow up into him in all things, which is the head, even Christ: From whom the whole body fitly joined together and compacted by that which every joint supplieth, according to the effectual working in the measure of every part, maketh increase of the body unto the edifying of itself in love.” (Ephesians 4:12-16). 

The Lord Jesus “…loved the church, and gave himself for it.” (Ephesians 5:25).  He is “…the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence.” (Colossians 1:18).  He is “…the chief corner stone.” (Ephesians 2:20).  As such, the Lord has equipped His church with what it needs to grow and flourish.  He “…led captivity captive, and gave gifts unto men.” (Ephesians 4:8) so that the body might function properly and under His control. 

1 Corinthians 12:18 tells us, “But now hath God set the members every one of them in the body, as it hath pleased him.”  The Lord places the believers in His body, His church, as it pleases Him to cause the church to prosper in spiritual growth.  We learn here that the Lord places believers and their gifts in the places where they can use their gifts to serve the Lord. 

In Ephesians 4:11, we are told about the gift of the evangelist.  The Greek word for the evangelist is “euangelistḗs” and literally means “a preacher of the Gospel.”  The evangelist seems to have a great burden for the lost and a great desire to share the Gospel with them.  If one has the gift of the evangelist, he would need to develop that gift through prayer, learning, obedience, and activity to effectively serve the Lord.  We read in 1 Timothy 4:14, “Neglect not the gift that is in thee…”  If the Lord has given us that gift, we need to begin to use it as He leads us so that we might become more proficient.  While there are examples of some being sent out to different or foreign lands to evangelize (Mark 16:15, Acts 8:5, 2 Corinthians 10:14, etc.), the evangelist does not necessarily have to travel to find those in need of salvation.  The needs of those around us are great and the Lord may use an evangelist to stay in his own hometown and spread the Gospel.

The Lord once met a man who was called Legion because he was possessed of many demons.  The Lord drove the demons from that man.  Afterwards, Legion desired to travel with the Lord in His journeys, but the Lord instructed him differently.  We read in Mark 5:18-20, “And when he was come into the ship, he that had been possessed with the devil prayed him that he might be with him. Howbeit Jesus suffered him not, but saith unto him, Go home to thy friends, and tell them how great things the Lord hath done for thee, and hath had compassion on thee. And he departed, and began to publish in Decapolis how great things Jesus had done for him: and all men did marvel.”  Here, the Lord wanted this man to stay close to home to tell others “how great things Jesus had done for him.” 

So, yes, there is a spiritual gift of witnessing to others.  It is called an evangelist.  Of course, all believers, while having some gift, do not have the gift of evangelism.  Yet, we read in 2 Timothy 4:5 that we should all, “…do the work of an evangelist.”  ALL BELIEVERS should be involved in sharing the Gospel with the lost.  We cannot leave it up to a few to tell others of their need of salvation.  “For whosoever shall call upon the name of the Lord shall be saved. How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher? And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!” (Romans 10:13-15).  Are you saved?  If so, you have been sent to tell others. (CC)  (582.2)