If you read Revelation 13:15-18, the mark of the beast or the name of the beast or the number of the beast has to be in the right hand or in the forehead.  The Covid-19 vaccine is not being give in those locations; it is given in the left shoulder so it cannot be the mark of the beast.  

Secondly, the mark of the beast is used to buy and sell which hasn't happened with the Covid-19 vaccine. The beast (antichrist) hasn't been revealed yet, and there is no image of the beast to worship by those who took the Covid-19 vaccine in the shoulder.  The image of the beast will be worshipped by those who take the mark of the beast in the right hand or in the forehead, and anyone not worshipping the image of the beast will not take the mark of the beast and will be killed.  So the Covid-19 vaccine is definitely not the mark of the beast.