ummm spice does not really need an api ..... spice simulation file looks something like this
LPFILTER.CIR - SIMPLE RC LOW-PASS FILTER
VS 1 0 AC 1 SIN(0VOFF 1VPEAK 2KHZ)
R1 1 2 1K
C1 2 0 0.032UF
.AC DEC 5 10 10MEG
.TRAN 5US 500US
* VIEW RESULTS
.PRINT AC VM(2) VP(2)
.PRINT TRAN V(1) V(2)
everything is driven by text files in the background and these files are passed to a pspice exe that normally does the rest. The spice engine itself is available with a BSD license so you can tweak it yourself.
Most commercial offerings offer schematic entry, parts libraries and output plotting options.
You can do away with this be passing in a netlist file with the simulation details to an spice engine and get back a text file of results.
So no real apil just a command line driven app. Of course you can get the source code and compile it into you own application.
check out wikipedia for more details.