Although methotrexate has been used for years now to treat psoriatic arthritis (PsA) with the impression of good effectiveness in both treating physicians, and patients, there has been scant proof of such effectiveness. The latest and most comprehensive data we have is from the 2012 MIPA trial 
The MIPA trial was a placebo-controlled study involving 221
methotrexate-naive individuals with PsA enrolled in 22 European
centers over a period of 5 years. Initial methotrexate at 7.5 mg per
week was increased to 10 mg per week at week 4, and to a target dose
of 15 mg per week at week 8. In individuals with persistently active
disease, the dose could be adjusted to 20 mg per week at 4 months and
25 mg per week at 5 months. Concomitant NSAIDs were allowed, but not
systemic glucocorticoids or other immunomodulatory agents. Response to
treatment was assessed at 3 months and 6 months. Of 109 people in the
methotrexate arm, only 67 were 'valid compliant completers', compared
with 61 of 112 in the placebo arm.
Although intention to treat analyses found significant improvement in physician and patient global assessments, there was no difference between placebo and active treatment in measures such as ESR, CRP, tender and swollen joint counts, and HAQ scores.
There has been some criticism of the trial including that the dose of methotrexate was escalated too slowly, and only 11% of subjects received doses greater than 15 mg per week, whereas 20 - 25 mg per week is more commonly used in the USA.
Nevertheless we lack good evidence currently for the efficacy of methotrexate in PsA, and perhaps patients should be first trialled on Leflunomide for which we do have efficacy data. 
 Kingsley GH, Kowalczyk A, Taylor H, [..], Scott DL. A randomized placebo-controlled trial of methotrexate in psoriatic arthritis. Rheumatology (Oxford). 2012 Aug;51(8):1368-77. doi: 10.1093/rheumatology/kes001. PubMed PMID: 22344575.
 Kaltwasser JP, Nash P, Gladman D, [..], Mease P. Efficacy and safety of leflunomide in the treatment of psoriatic arthritis and psoriasis: a multinational, double-blind, randomized, placebo-controlled clinical trial. Arthritis Rheum. 2004 Jun;50(6):1939-50. doi: 10.1002/art.20253. PubMed PMID: 15188371.