Problems with your approach.
C strings must end in 0 byte, in other words '\0' character. Using "" adds that automatically, but otherwise you have to add it yourself, and all string functions depend on that 0 being there.
Your v array contains characters, not strings, and strcat takes strings.
One solution:
char cmd[50] = "some text here";
char *v[] = {"a","s","d","c","b"};
strcat(cmd,v[3]);
This turns your char array into array of pointers to C strings.
Also, it's your responsibility to take care that, cmd[] contains enough space to hold whatever you add to it with strcat (here it does). It's usually best to use snprintf to do string concatenation, as it takes total size of the target array including terminating null, and adds that null there always, so it's harder to mess up. Example with your original char array:
char cmd[50] = "some text here";
char buf[50];
char v[] = {'a','s','d','c','b'};
snprintf(buf, sizeof buf, "%s%c", cmd, v[3]);
Notes: sizeof like this works only when buf really is an array, declared with [] like here. Also with snprintf, using same buffer both as destination and format argument may yield unexpected results, so I added a new destination buffer variable.
One more snprintf example, with your original two arrays only, appending to end of current contents of cmd:
snprintf(cmd + strlen(cmd), (sizeof cmd) - strlen(cmd), "%c", v[3]);
So clearly, in this particular case, the strncat(cmd, &v[3], 1) suggested in other answers to add 1 character is much nicer, but benefit of snprintf is, you can add all datatype supported by printf, not chars.