I've already compiled with -fPIC, so what's wrong?
That part of the error message is for people who are linking compiler-generated code.
You're writing asm by hand, so as datenwolf correctly wrote, when writing a shared library in assembly, you have to take care for yourself that the code is position independent.
This means file must not contain any 32-bit absolute addresses (because relocation to an arbitrary 64-bit base is impossible).  64-bit absolute relocations are supported, but normally you should only use that for jump tables.
mov var1, %rcx uses a 32-bit absolute addressing mode.  You should normally never do this, even in position-dependent x86-64 code.  The normal use-cases for 32-bit absolute addresses are:  putting an address into a 64-bit register withmov $var1, %edi (zero-extends into RDI)
and indexing static arrays: mov arr(,%rdx,4), %edx
mov var1(%rip), %rcx uses a RIP-relative 32-bit offset.  It's the efficient way to address static data, and compilers always use this even without -fPIE or -fPIC for static/global variables.
You have basically two possibilities: 
- Normal library-private static data, like C compilers will make for - __attribute__((visibility("hidden"))) long var1;, same as for- -fno-PIC.
 - .data
    .globl var1       # linkable from other .o files in the same shared object / library
    .hidden var1      # not visible for *dynamic* linking outside the library
var1:
    .quad     0x012345
.text
    .globl func1
func1:
    xor  %eax, %eax             # return 0
    mov  var1(%rip), %rcx   
    ret
 
- full symbol-interposition-aware code like compilers generate for - -fPIC.
 - You have to use the Global Offset Table. This is how a compiler does it, if you tell him to produce code for a shared library.
Note that this comes with a performance hit because of the additional indirection.  - See Sorry state of dynamic libraries on Linux for more about symbol-interposition and the overheads it imposes on code-gen for shared libraries if you're not careful about restricting symbol visibility to allow inlining. - var1@GOTPCRELis the address of a pointer to your- var1, the pointer itself is reachable with rip-relative addressing, while the content (the address of- var1) is filled by the linker during loading of the library.  This supports the case where the program using your library defined- var1, so- var1in your library should resolve to that memory location instead of the one in the- .dataor- .bss(or- .text) of your- .so.
 -     .section .data
    .globl var1
    # without .hidden
var1:
    .quad     0x012345
    .section .text
    .globl func1
func1:
    xor %eax, %eax
    mov var1@GOTPCREL(%rip), %rcx
    mov (%rcx), %rcx
    ret
 
See some additional information at http://www.bottomupcs.com/global_offset_tables.html 
An example on the Godbolt compiler explorer of -fPIC vs. -fPIE shows the difference that symbol-interposition makes for getting the address of non-hidden global variables:
- movl    $x, %eax5 bytes,- -fno-pie
- leaq    x(%rip), %rax7 bytes,- -fPIEand hidden globals or- staticwith- -fPIC
- y@GOTPCREL(%rip), %rax7 bytes and a load instead of just ALU,- -fPICwith non-hidden globals.
Actually loading always uses x(%rip), except for non-hidden / non-static vars with -fPIC where it has to get the runtime address from the GOT first, because it's not a link-time constant offset relative to the code.
Related: 32-bit absolute addresses no longer allowed in x86-64 Linux? (PIE executables).
A previous version of this answer stated that the DATA and BSS segments could move relative to TEXT when loading a dynamic library.  This is incorrect, only the library base address is relocatable.  RIP-relative access to other segments within the same library is guaranteed to be ok, and compilers emit code that does this.  The ELF headers specify how the segments (which contain the sections) need to be loaded/mapped into memory.