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According to the CGI article on Memory Alpha:

The very first CGI used was in Star Trek II: The Wrath of Khan, where Lucasfilm Graphics Group, then a subsidiary of Industrial Light & Magic (ILM), was responsible for the "Project Genesis" demonstration sequence effect, the very first fully textured 3D CGI representation shown in the motion picture business to a general public.

So per to the article, which is thoroughly detailed on the use of CGI in the franchise, the first use of a fully textured 3D CGI then would be the Genesis Effect, seen here (1982):

As luck would have it, there's actually "making of" video available on youtube:

According to the CGI article on Memory Alpha:

The very first CGI used was in Star Trek II: The Wrath of Khan, where Lucasfilm Graphics Group, then a subsidiary of Industrial Light & Magic (ILM), was responsible for the "Project Genesis" demonstration sequence effect, the very first fully textured 3D CGI representation shown in the motion picture business to a general public.

So per to the article, which is thoroughly detailed on the use of CGI in the franchise, the first use of a fully textured 3D CGI then would be the Genesis Effect, seen here (1982):

As luck would have it, there's actually "making of" video available on youtube:

According to the CGI article on Memory Alpha:

The very first CGI used was in Star Trek II: The Wrath of Khan, where Lucasfilm Graphics Group, then a subsidiary of Industrial Light & Magic (ILM), was responsible for the "Project Genesis" demonstration sequence effect, the very first fully textured 3D CGI representation shown in the motion picture business to a general public. The Graphics Group later evolved into Pixar, in 1986.

So per to the article, which is thoroughly detailed on the use of CGI in the franchise, the first use of a fully textured 3D CGI then would be the Genesis effect, seen here:

As luck would have it, there's actually "making of" video available on youtube:

According to the CGI article on Memory Alpha:

The very first CGI used was in Star Trek II: The Wrath of Khan, where Lucasfilm Graphics Group, then a subsidiary of Industrial Light & Magic (ILM), was responsible for the "Project Genesis" demonstration sequence effect, the very first fully textured 3D CGI representation shown in the motion picture business to a general public.

So per to the article, which is thoroughly detailed on the use of CGI in the franchise, the first use of a fully textured 3D CGI then would be the Genesis Effect, seen here (1982):

As luck would have it, there's actually "making of" video available on youtube:

According to the CGI article on Memory Alpha:

The very first CGI used was in Star Trek II: The Wrath of Khan, where Lucasfilm Graphics Group, then a subsidiary of Industrial Light & Magic (ILM), was responsible for the "Project Genesis" demonstration sequence effect, the very first fully textured 3D CGI representation shown in the motion picture business to a general public. The Graphics Group later evolved into Pixar, in 1986.

So per to the article, which is thoroughly detailed on the use of CGI in the franchise, the first use of a fully textured 3D CGI then would be the Genesis effect, seen here:

As luck would have it, there's actually "making of" video available on youtube:

According to the CGI article on Memory Alpha:

The very first CGI used was in Star Trek II: The Wrath of Khan, where Lucasfilm Graphics Group, then a subsidiary of Industrial Light & Magic (ILM), was responsible for the "Project Genesis" demonstration sequence effect, the very first fully textured 3D CGI representation shown in the motion picture business to a general public. The Graphics Group later evolved into Pixar, in 1986.

So per to the article, which is thoroughly detailed on the use of CGI in the franchise, the first use of a fully textured 3D CGI then would be the Genesis effect, seen here: 

As luck would have it, there's actually "making of" video available on youtube: