Is there a vim command to relocate a tab?

You can relocate a tab with :tabm using either relative or zero-index absolute arguments.

absolute:

• Move tab to position i: :tabm i

relative:

• Move tab i positions to the right: :tabm +i
• Move tab i positions to the left: :tabm -i

It's a relatively new feature. So if it doesn't work try updating your vim.

Do you mean moving the current tab? This works using tabmove.

:tabm[ove] [N]                                          *:tabm* *:tabmove*
            Move the current tab page to after tab page N.  Use zero to
            make the current tab page the first one.  Without N the tab
            page is made the last one.

I have two key bindings that move my current tab one left or one right. Very handy!

EDIT: Here is my VIM macro. I'm not a big ViM coder, so maybe it could be done better, but that's how it works for me:

" Move current tab into the specified direction.
"
" @param direction -1 for left, 1 for right.
function! TabMove(direction)
    " get number of tab pages.
    let ntp=tabpagenr("$")
    " move tab, if necessary.
    if ntp > 1
        " get number of current tab page.
        let ctpn=tabpagenr()
        " move left.
        if a:direction < 0
            let index=((ctpn-1+ntp-1)%ntp)
        else
            let index=(ctpn%ntp)
        endif

        " move tab page.
        execute "tabmove ".index
    endif
endfunction

After this you can bind keys, for example like this in your .vimrc:

map <F9> :call TabMove(-1)<CR>
map <F10> :call TabMove(1)<CR>

Now you can move your current tab by pressing F9 or F10.

I was looking for the same and after some posts I found a simpler way than a function:

:execute "tabmove" tabpagenr() # Move the tab to the right
:execute "tabmove" tabpagenr() - 2 # Move the tab to the left

The tabpagenr() returns the actual tab position, and tabmove uses indexes.

I mapped the right to Ctrl+L and the left to Ctrl+H:

map <C-H> :execute "tabmove" tabpagenr() - 2 <CR>
map <C-J> :execute "tabmove" tabpagenr() <CR>